Ooops!!! there is no difference in die() and exit(). die() is equivalent to exit and vice versa. But why these two names because of there are functions which changed names because of an API cleanup or some other reason and the old names are only kept as aliases for backward compatibility. 
php.net says
There are quite a few functions in PHP which you can call with more than one name. In some cases there is no preferred name among the multiple ones, is_int() and is_integer() are equally good for example. However there are functions which changed names because of an API cleanup or some other reason and the old names are only kept as aliases for backward compatibility. It is usually a bad idea to use these kind of aliases, as they may be bound to obsolescence or renaming, which will lead to unportable script. This list is provided to help those who want to upgrade their old scripts to newer syntax.
References
http://php.net/manual/en/aliases.php
http://www.php.net/manual/en/ref.misc.php
