Whether some thing is declared in header file or in source file makes absolutely no difference for the compiler. In fact, the compiler proper knows absolutely nothing about any "header files", since header files are embedded into source files by so called preprocessor, which does its work before the compiler proper. By the time the source files (with embedded header files) get to the actual compiler, there's no way to tell what was there originally and what was inserted from header files. The source file with all the header files embedded into it is called translation unit. I.e. the compiler proper works with translation units, not with some "source" or "header" files.
In C language all objects and functions declared at file scope have external linkage by default, which means that they are global, unique for the entire program. So, you thought incorrectly. Functions are not local to one source file only.
If you want to make a function (or an object) local to a single translation unit, you have to take some explicit steps. You have to declare it as static
. Declaring it as static will give it internal linkage, which essentially means that it becomes internal to its translation unit.
Declaring your functions static
will only work if both of them really have to be local to their own translation units. If this is not the case, i.e. if at least one of the functions should be a globally accessible (linkable) function, then you have no other choice but to rename one of functions.