Rebbi is just Rebbi, without the definite article. “The rebbe” depends on the context, exactly like “the rosh yeshivah”, “the rav”, or “the president”. Why do you not ask about those?
in most cases when one says the rebbe without specifying which one they are reffering to the lubavitcher rebbe edited
for example a google search the rebbe brings up the lubavutcheer rebbe