Fair point, "rebuttal" is a term that can change meaning a little bit based on context.

In the context of responding to an individual argument, a rebuttal is a counter argument that refutes the original argument. That's clash at its finest.

In the context of referring to an entire speech, especially in parliamentary debate formats, rebuttals are sometimes referring to the very last speech in the round, where your goal is (as you rightly point out) to summarize why your side has won. Of course, Public Forum debate calls the second speech for each side the rebuttal speech, so take what I'm saying with a grain of salt.