If bool is a macro for int, why is it a different size?

I was hoping somebody could explain why

#include <stdbool.h>

printf("size of bool %d\n", sizeof(bool));
printf("size of int %d\n", sizeof(int));

outputs to

size of bool 1
size of int 4

I've looked at http://pubs.opengroup.org/onlinepubs/009695399/basedefs/stdbool.h.html which seems to indicate that bool is essentially a macro for _Bool which, when set to true or false, is really just a macro for an integer constant. If it is an integer, why is it not the same size?

I'm asking because it took us far too long to debug a program for which we did not allocate enough memory.