How do Unix Domain Sockets differentiate between multiple clients?

If you create a PF_UNIX socket of type SOCK_STREAM, and accept connections on it, then each time you accept a connection, you get a new file descriptor (as the return value of the accept system call). This file descriptor reads data from and writes data to a file descriptor in the client process. Thus it works just like a TCP/IP connection.

There's no “unix domain protocol format”. There doesn't need to be, because a Unix-domain socket can't be connected to a peer over a network connection. In the kernel, the file descriptor representing your end of a SOCK_STREAM Unix-domain socket points to a data structure that tells the kernel which file descriptor is at the other end of the connection. When you write data to your file descriptor, the kernel looks up the file descriptor at the other end of the connection and appends the data to that other file descriptor's read buffer. The kernel doesn't need to put your data inside a packet with a header describing its destination.

For a SOCK_DGRAM socket, you have to tell the kernel the path of the socket that should receive your data, and it uses that to look up the file descriptor for that receiving socket.

If you bind a path to your client socket before you connect to the server socket (or before you send data if you're using SOCK_DGRAM), then the server process can get that path using getpeername (for SOCK_STREAM). For a SOCK_DGRAM, the receiving side can use recvfrom to get the path of the sending socket.

If you don't bind a path, then the receiving process can't get an id that uniquely identifies the peer. At least, not on the Linux kernel I'm running (2.6.18-238.19.1.el5).