Function definition etc is a formal term, but "implementation" is a fuzzy informal term. In plain English, it could refer to your application's implementation of something, like for example a function. The implementation phase of a project is typically the phase where you write all the code. And so on - it depends on context.
In formal/technical C programming terms, implementation means the implementation of the C language. That is: formally implementation means the C compiler and standard library. And the formal term implementation-defined behavior means compiler-specific behavior.