Asking the important questions
To both of you: I'm pretty sure the "but paid" versions are to keep minors off the game on easy access platforms like android where you can just search "tentacle locker 2 itch io" and get this after some digging. More than likely, the "but paid" versions are much cheaper and only require around 2-5 dollars whereas the patreon version would require 10-15 dollars. Take that with a grain of salt because I don't know which versions are paid, thw cost of patreon and normal versions, etc. Just going off of what I know from tentacle locker 2 and what you just said.
Edit: I am right; but 10$ but paid and 16$ patreon. Also, but paid here gives more content earlier, and patreon gives more content earlier for all Katwhorm games. Imagine a standard, premium, and premium bundle (normal, paid, patreon).
Perhaps not in this game as i havent gotten to play it yet, or this persons other games. However, going by things i already know both as a customer and previously a game dev on newgrounds that this is most likely what is happening.
TL;DR: No, but you get access to updates earlier, and unlike "but paid", patreon gives that for all katwhorm's games. (In theory)