The best way to prove that it was a ransom is to find someone involved in the negotiations who will say it was for ransom. Another way to prove that the money was for ransom would be to prove that the US still owes Iran the 400 million for a refund of the money Iran once paid for weapons that they never received.
Instead of "rather than," it can be both. Was the release of the hostages contingent on receipt of the funds? If yes, then it's ransom. It doesn't matter if we owed them the money or not - an issue that has been under dispute for decades.