From Storage-class specifiers:
The storage-class specifiers determine two independent properties of the names they declare: storage duration and linkage.
So, for example, when static keyword is used on global variables and functions (who's storage class is static anyway) it sets their linkage to Internal-linkage. When used on variables inside functions (which have no linkage) - it sets their storage class to static.
My question is: why is the same specifier used for both things?
The reason is mostly historical: linkage came into the design of C language as an afterthought. In the early versions you could redeclare global variables as many times as you wish, and linker would merge all these declarations for you:
Ritchie's original intention had been to model C's rules on FORTRAN COMMON declarations, on the theory that any machine that could handle FORTRAN would be ready for C. In the common-block model, a public variable may be declared multiple times; identical declarations are merged by the linker. (source)
The current rule of a single declaration came later, along with extern keyword. At that point there was a body of C code significant enough to make backward compatibility important. That is probably the reason why language designers refrained from introducing a new keyword for handling linkage, reusing static instead.