You should look up the details of the types defined in the C99 header <stdint.h>. It conditionally defines types like int32_t (it won't be defined if the machine has no 32-bit type — fairly unlikely these days, but there are/were 36-bit machines in times past), and unconditionally defines types such as int_least32_t and int_fast32_t. The type int_least32_t is an alternative name for a type that is at least 32 bits wide; int_fast32_t is an alternative name for the fastest type that is at least 32 bits wide. These types must be supported in C99 because long must be at least 32 bits wide.
So, the names in use are carefully chosen from the C99 standard.