The socket functions send information directly over the Internet Protocol. They operate at a much lower level compared to fsockopen and streams. Generally, they wrap C functions of the same name. If you have experience programming for sockets in C, these functions will be familiar. A full discussion of sockets programming is out of scope.
Use of these functions implies solving a problem that the higher level functions can't address. In other words, it makes little sense to use these functions to implement functionality provided by fopen. You may find them most useful when using PHP in a nontraditional way, such as starting an Internet daemon from the CLI (command-line interface) version of PHP.