Buying/trading spot coins on exchanges with usdt vs usdc or another stable coin

Does it matter which stable coin you use to buy/trade spot coins on exchanges? For instance is there a difference between btc/usdt and btc/usdc? If usdt get default/depeg etc, you wont lose your btc you got with usdt on exchange, right?

Most coins in exchanges are traded with usdt and some with usdc or both. Just wanna make sure we wont be screwed because of something stupid like this. This shouldnt happen because once you get your coin you pay it with stable coin and you dont have any relation with that stable coin anymore. Am i missing something? Thanks.