As I understand it, the C specification says that type int is supposed to be the most efficient type on target platform that contains at least 16 bits.
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The difference is that the fast types are allowed to be wider than their counterparts (without fast) for efficiency/optimization purposes. But the C standard by no means guarantees they are actually faster.
C11, 7.20.1.3 Fastest minimum-width integer types
1 Each of the following types designates an integer type that is usually fastest 262) to operate with among all integer types that have at least the specified width.
2 The typedef name int_fastN_t designates the fastest signed integer type with a width of at least N. The typedef name uint_fastN_t designates the fastest unsigned integer type with a width of at least N.
262) The designated type is not guaranteed to be fastest for all purposes; if the implementation has no clear grounds for choosing one type over another, it will simply pick some integer type satisfying the signedness and width requirements.
Another difference is that fast and least types are required types whereas other exact width types are optional:
3 The following types are required: int_fast8_t int_fast16_t int_fast32_t int_fast64_t uint_fast8_t uint_fast16_t uint_fast32_t uint_fast64_t All other types of this form are optional.