In practice I think it doesn’t matter so much.
Once we have a conflict and an intent you get a task which in these social cases are the speech and actions taken by the character. The GM will call “Make a persuasion test” or whatever and a player might ask “I thought this would be rhetoric perhaps?”. The GM can ask “how is that rhetoric?” and the player can make a brief case for why the character’s actions was rhetoric. The GM decides but ultimately it doesn’t matter in that way.
In Torchbearer and Mouse Guard social tests are mostly handled by Persuader, Manipulator and Orator because there isn’t the need for nuance.
In Burning Wheel the skill written on the sheet informs the play. The important thing about having Stentorious Debate on your character sheet isn’t that it’s open ended, it’s that you will argy-barge like a dwarf and not whisper subtleties like spy because you don’t want the GM to say “that sounds like persuasion!”
Edit: As you get used to what the players have on their sheets and you get to know the characters you will recognise the skills the player is intending to use. But you still need to say “That’s an oratory test.” when it applies even if that wasn’t what they were expecting.