int_T, real_T (upper case T) are data types used by MATLAB and Simulink and are defined in shipped file "tmwtypes.h". They prove more flexibility in terms of platform dependency. For example real_T can switch types for 32 or 64 bit systems. To define a custom S-Function in C, you need not use any of these data types and can use standard ones like int, double etc.
I think you can also use int_t (small case t) in your code as long as those definitions are provided to MATLAB.