C++ sometimes uses the suffix _type on type definitions (e.g. std::vector),
also sometimes _t (e.g. std::si
As a C heritage the _t (that used to mean "defined via typedef") syntax has been inherited (they're also SUS/POSIX-reserved in the global namespace).
Types added in C++ and not present in the original C language (e.g. size_type) don't need to be shortened.
Keep in mind that to the best of my knowledge this is more of an observation on an established convention rather than a general rule.