There's nothing special about threads vs processes in Linux. mmap works the same, the challenge is to map the same file. You can share a path, pass a file descriptor via fork or unix domain socket, among other techniques.
As long as we're pedantic ... the subject is shared memory. Unless you specify the same, non-null, target address in the call to mmap (and the kernel happens to grant you that mapping on all calling sites), the addresses will be different; the address space is not shared (each mapping might also have different access permissions).
That distinction is important as pointers generally cannot be shared (a problem which can of course be solved with one more indirection ;-) .
Yeah that's true, and I'd say threads need synchronization for concurrent access too, but supposedly the options for doing that are faster than what you need to use across processes.