Yes, that’s the usual application, but it’s the wrong level of generality to make them synonyms. “Fully general counterargument” is one particular absurdity that you can reduce things to. Even after you’ve specified that you’re performing a reductio ad absurdum against the proposition “argument X is sound”, you still need to say what the absurd conclusion is, so you still need a term for “fully general counterargument”.
Yes, that’s the usual application, but it’s the wrong level of generality to make them synonyms. “Fully general counterargument” is one particular absurdity that you can reduce things to. Even after you’ve specified that you’re performing a reductio ad absurdum against the proposition “argument X is sound”, you still need to say what the absurd conclusion is, so you still need a term for “fully general counterargument”.