Both are same and equivalent, both are centralize. USDT and USDC is stablecoin pegged to USD. So, no worries.
Why do you think that some brokers does not have BTC/USD? For example, Binance. They have BTC/USDT and BTC/USDC but not BTC/USD.
Because USD deposit methods are very few when it comes to international business, there are regulations too.
USDT - Crypto
USDC - Crypto
USD- Fiat.
All threes are same man, they look like crypto but they are not. They are centrally controlled, risk are there.