Why were short, int, and long invented in C?

Question

I'm having trouble understanding, what were the exact purposes of creating the short, int, and long data types in C?

The reason I ask is, it doesn't seem like their sizes are bounded -- they could be of any size, so long as short is smaller than an int, for example.

In which situations, then, should you use an unsigned int or unsigned long, for example, instead of a size_t, when doing so offers no hope of binary compatibility?

(If you don't know the size, then how would you know when to choose which?)