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There are two types of quotes in MySQL:

1. 
   ' for enclosing string literals


2. 
   ` for enclosing identifiers such as table and column names

And then there is " which is a special case. It could be used for one of above-mentioned purposes at a time depending on MySQL server's sql_mode:

1. 
   By default the " character can be used to enclose string literals just like '
   


2. In ANSI_QUOTES mode the " character can be used to enclose identifiers just like `
   

The following query will produce different results (or errors) depending on SQL mode:

SELECT "column" FROM table WHERE foo = "bar"

ANSI_QUOTES disabled

The query will select the string literal "column" where column foo is equal to string "bar"

ANSI_QUOTES enabled

The query will select the column column where column foo is equal to column bar

When to use what

• I suggest that you avoid using " so that your code becomes independent of SQL modes


• Always quote identifiers since it is a good practice (quite a few questions on SO discuss this)

(There are good answers above regarding the SQL nature of your question, but this may also be relevant if you are new to PHP.)

Perhaps it is important to mention that PHP handles single and double quoted strings differently...

Single-quoted strings are 'literals' and are pretty much WYSIWYG strings. Double-quoted strings are interpreted by PHP for possible variable-substitution (backticks in PHP are not exactly strings; they execute a command in the shell and return the result).

Examples:

$foo = "bar";
echo 'there is a $foo'; // There is a $foo
echo "there is a $foo"; // There is a bar
echo `ls -l`; // ... a directory list

Backticks are generally used to indicate an identifier and as well be safe from accidentally using the Reserved Keywords.

For example:

Use `database`;

Here the backticks will help the server to understand that the database is in fact the name of the database, not the database identifier.

Same can be done for the table names and field names. This is a very good habit if you wrap your database identifier with backticks.

Check this answer to understand more about backticks.

Now about Double quotes & Single Quotes (Michael has already mentioned that).

But, to define a value you have to use either single or double quotes. Lets see another example.

INSERT INTO `tablename` (`id, `title`) VALUES ( NULL, title1);

Here I have deliberately forgotten to wrap the title1 with quotes. Now the server will take the title1 as a column name (i.e. an identifier). So, to indicate that it's a value you have to use either double or single quotes.

INSERT INTO `tablename` (`id, `title`) VALUES ( NULL, 'title1');

Now, in combination with PHP, double quotes and single quotes make your query writing time much easier. Let's see a modified version of the query in your question.

$query = "INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, '$val1', '$val2')";

Now, using double quotes in the PHP, you will make the variables $val1, and $val2 to use their values thus creating a perfectly valid query. Like

$val1 = "my value 1";
$val2 = "my value 2";
$query = "INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, '$val1', '$val2')";

will make

INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, 'my value 1', 'my value 2')

Basically in Mysql, There are these kinds of identifier are used in query ` ," ,' and () .

1. " or ' use for enclosing the string like values "26-01-2014 00:00:00" or '26-01-2014 00:00:00' . These identifier use only for string not aggregate function like now() or sum ,max etc.




2. ` use for enclosing table or table column e.g. select column_name from table_name where id='2'




3. () are use only for just enclose parts of query e.g. select column_name from table_name where (id='2' and gender='male') or name='rakesh' .

The string literals in MySQL and PHP are the same.

A string is a sequence of bytes or characters, enclosed within either
single quote (“'”) or double quote (“"”) characters.

So if your string contains single quotes, then you could use double quotes to quote the string, or if it contains double quotes, then you could use single quotes to quote the string. But if your string contains both single quotes and double quotes, you need to escape the one that used to quote the string.

Mostly, we use single quotes for an SQL string value, so we need to use double quotes for a PHP string.

$query = "INSERT INTO table (id, col1, col2) VALUES (NULL, 'val1', 'val2')";

And you could use a variable in PHP's double-quoted string:

$query = "INSERT INTO table (id, col1, col2) VALUES (NULL, '$val1', '$val2')";

But if $val1 or $val2 contains single quotes, that will make your SQL be wrong. So you need to escape it before it is used in sql; that is what mysql_real_escape_string is for. (Although a prepared statement is better.)

In combination of PHP and MySQL, double quotes and single quotes make your query-writing time so much easier.

$query = "INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, '$val1', '$val2')";

Now, suppose you are using a direct post variable into the MySQL query then, use it this way:

$query = "INSERT INTO `table` (`id`, `name`, `email`) VALUES (' ".$_POST['id']." ', ' ".$_POST['name']." ', ' ".$_POST['email']." ')";

This is the best practice for using PHP variables into MySQL.

If table cols and values are variables then there are two ways:

With double quotes "" the complete query:

$query = "INSERT INTO $table_name (id, $col1, $col2)
 VALUES (NULL, '$val1', '$val2')";

Or

 $query = "INSERT INTO ".$table_name." (id, ".$col1.", ".$col2.")
 VALUES (NULL, '".$val1."', '".$val2."')";

With single quotes '':

$query = 'INSERT INTO '.$table_name.' (id, '.$col1.', '.$col2.')
 VALUES (NULL, '.$val1.', '.$val2.')';

Use back ticks `` when a column/value name is similar to a MySQL reserved keyword.

Note: If you are denoting a column name with a table name then use back ticks like this:

`table_name`. `column_name` <-- Note: exclude . from back ticks.

There has been many helpful answers here, generally culminating into two points.

1. BACKTICKS(`) are used around identifier names.


2. SINGLE QUOTES(') are used around values.

AND as @MichaelBerkowski said

Backticks are to be used for table and column identifiers, but are
only necessary when the identifier is a MySQL reserved keyword, or
when the identifier contains whitespace characters or characters
beyond a limited set (see below) It is often recommended to avoid
using reserved keywords as column or table identifiers when possible,
avoiding the quoting issue.

There is a case though where an identifier can neither be a reserved keyword or contain whitespace or characters beyond limited set but necessarily require backticks around them.

EXAMPLE

123E10 is a valid identifier name but also a valid INTEGER literal.

[Without going into detail how you would get such an identifier name], Suppose I want to create a temporary table named 123456e6.

No ERROR on backticks.

DB [XXX]> create temporary table `123456e6` (`id` char (8));
Query OK, 0 rows affected (0.03 sec)

ERROR when not using backticks.

DB [XXX]> create temporary table 123451e6 (`id` char (8));
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near '123451e6 (`id` char (8))' at line 1

However, 123451a6 is a perfectly fine identifier name (without back ticks).

DB [XXX]> create temporary table 123451a6 (`id` char (8));
Query OK, 0 rows affected (0.03 sec)

This is completely because 1234156e6 is also an exponential number.

Single quotes should be used for string values like in the VALUES() list.

Backticks are generally used to indicate an identifier and as well be safe from accidentally using the reserved keywords.

In combination of PHP and MySQL, double quotes and single quotes make your query writing time so much easier.

Besides all of the (well-explained) answers, there hasn't been the following mentioned and I visit this Q&A quite often.

In a nutshell; MySQL thinks you want to do math on its own table/column and interprets hyphens such as "e-mail" as e minus mail.

Disclaimer: So I thought I would add this as an "FYI" type of answer for those who are completely new to working with databases and who may not understand the technical terms described already.

SQL servers and MySQL, PostgreySQL, Oracle don't understand double quotes("). Thus your query should be free from double quotes(") and should only use single quotes(').

Back-trip(`) is optional to use in SQL and is used for table name, db name and column names.

If you are trying to write query in your back-end to call MySQL then you can use double quote(") or single quotes(') to assign query to a variable like:

let query = "select id, name from accounts";
//Or
let query = 'select id, name from accounts';

If ther's a where statement in your query and/or trying to insert a value and/or an update of value which is string use single quote(') for these values like:

let querySelect = "select id, name from accounts where name = 'John'";
let queryUpdate = "update accounts set name = 'John' where id = 8";
let queryInsert = "insert into accounts(name) values('John')";

//Please not that double quotes are only to be used in assigning string to our variable not in the query
//All these below will generate error

let querySelect = 'select id, name from accounts where name = "John"';
let queryUpdate = 'update accounts set name = "John" where id = 8';
let queryInsert = 'insert into accounts(name) values("John")';

//As MySQL or any SQL doesn't understand double quotes("), these all will generate error.

If you want to stay out of this confusion when to use double quotes(") and single quotes('), would recommend to stick with single quotes(') this will include backslash() like:

let query = 'select is, name from accounts where name = 'John'';

Problem with double(") or single(') quotes arise when we had to assign some value dynamic and perform some string concatenation like:

let query = "select id, name from accounts where name = " + fName + " " + lName;
//This will generate error as it must be like name = 'John Smith' for SQL
//However our statement made it like name = John Smith

//In order to resolve such errors use
let query = "select id, name from accounts where name = '" + fName + " " + lName + "'";

//Or using backslash()
let query = 'select id, name from accounts where name = '' + fName + ' ' + lName + ''';

If need further clearance do follow quotes in JavaScript