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What is the difference between the two linux syscalls set_tid_address and set_thread_area?

Which one (on x86-64 long mode) updates the fs register?

arch_prctl sets the fs register.

To expand on Korona's answer: arch_prctl() can set FS on x86_64. set_thread_area() was the old system call for 32-bit applications to install a thread-local GDT segment that can point anywhere, and that you can then load yourself into whatever segment you wish. set_tid_address() is something else entirely. It sets an address meant to hold the thread's TID. When the thread exits, the kernel sets that address to 0 and performs a futex-wake on the address. This can be used to implement threading libraries. For instance, you can implement pthread_join() by having one thread wait on the TID address of the other thread.