They are completely different. fsockopen opens a socket (the type of socket depending on the protocol prefix). fopen opens a file or sometimes something else (like a file over HTTP, or a stream filter or something).
But I believe that the set of things which can be opened with them has little (if any) overlap.
However, once it's open, you can do most of the same things on the resulting handle (depending on how you opened it; if it's opened for reading only, you can't write, obviously). For some types of object, some operations don't make sense (such as using fseek() on a socket)
Mark