Networking is an integral part of PHP's capability as a web language, and its implementation of various networking capabilities is unsurprisingly vast - you could write a book on PHP networking alone.
Although fopen() allows you to work with HTTP and FTP, using the more specific functions allows you to take full advantage of PHP's capabilities - particular with FTP, all the really good stuff is only accessible from the dedicated FTP functions.
Curl is a powerful and flexible way to handle a number of network protocols through one programming interface. We've only scratched the surface here; a more detailed examination on your behalf will certainly yield big results!
LDAP is a trusted and popular network protocol that's in use around the world in large companies to help them organise their workforce. With PHP, LDAP finds a home outside its traditional areas (eg mail clients), and there are many cool applications for it there.