"t" means "type" (or to some people, typedef, which is the command used to create them). size_t is the type used to specify memory sizes. time_t on the other hand, is the type used to specify time spans. They generally happen to refer to the same underlying type (a 64-bit or 32-bit integer, depending on the platform), but the label helps keep them straight conceptually so that the implementation details can be hammered out by the compiler.

For example, time_t used to be a 32-bit integer, meaning that the clock would roll over in 2038. But on most 64-bit architectures, they've expanded time_t to be a 64-bit integer, which means that 64-bit systems won't have a "year-2038" problem. Since code that deals with unix timestamps uses the type name time_t rather than int to refer to these values, everything will "just work" when you simply recompile the code for your new architecture.