If I include
or
in a C program I don\'t have to link these when compiling but I do have to link to
There's a thorough discussion of linking to external libraries in An Introduction to GCC - Linking with external libraries. If a library is a member of the standard libraries (like stdio), then you don't need to specify to the compiler (really the linker) to link them.
EDIT: After reading some of the other answers and comments, I think the libc.a reference and the libm reference that it links to both have a lot to say about why the two are separate.
Note that many of the functions in 'libm.a' (the math library) are defined in 'math.h' but are not present in libc.a. Some are, which may get confusing, but the rule of thumb is this--the C library contains those functions that ANSI dictates must exist, so that you don't need the -lm if you only use ANSI functions. In contrast, `libm.a' contains more functions and supports additional functionality such as the matherr call-back and compliance to several alternative standards of behavior in case of FP errors. See section libm, for more details.