I think that functionality was inherited from the keyboard driver in the original IBM BIOS.
As far as I recall there is a functional difference between ctrl-s in a terminal and the pause key in BIOS/DOS/Windows.
The ctrl-s key combination only affects the terminal. The process can keep running unaffected after you press ctrl-s until it tries to write to the terminal. Only then will it block on the write system call. If a process is busy doing some processing with no output to the terminal, that can continue after pressing ctrl-s.
The pause key will however block the processing entirely. As I recall it, once pause is pressed an interrupt is generated. And control flow does not return to the running process after that. Instead the keyboard driver will wait for a different key to be pressed before returning to the program context which was interrupted by the pause key.