What exactly is the difference between the is_callable and function_exists in PHP?

The function is_callable accepts not only function names, but also other types of callbacks:

• Foo::method
• array("Foo", "method")
• array($obj, "method")
• Closures and other invokable objects (PHP 5.3)

So is_callable accepts anything that you could pass call_user_func and family, while function_exists only tells if a certain function exists (not methods, see method_exists for that, nor closures).

Put another way, is_callable is a wrapper for zend_is_callable, which handles variables with the pseudo-type callback, while function_exists only does a hash table lookup in the functions’ table.