A wallet that supports TRC20 lists TRON, or TRC20 by name, in its network menu for receiving and sending; support for USDT on some network is not enough. Checking takes a moment: open the screen for receiving USDT and read the networks offered. Such a wallet also needs a way to pay TRON fees, whether TRX held in it, energy and bandwidth covering part of each transfer, or TRX burnt when those run short. The expected fee appears before confirming, and the casino cashier lists the networks it takes.
A TRC20 wallet address is an address on the TRON network, where USDT and other TRC20 tokens are received, and it usually starts with a capital T and runs to 34 characters. Addresses for BEP20 and ERC20 both start with 0x and can be exactly the same on those two chains. An address alone therefore does not reveal which network it belongs to. The network is chosen from a menu on both sides of the transfer, and USDT sent on one network does not appear on another by itself.
A blockchain explorer is a public website that reads a network's records and presents them in plain form: transfers, addresses, balances, fees and confirmations. Each network has its own, so a TRC20 transfer is looked up on a TRON explorer and a bitcoin transfer on a bitcoin one. Using a blockchain explorer needs no account, only a hash or address pasted into its search box. A screenshot proves nothing when the hash cannot be found there, while transfers inside one exchange may never reach the network and appear only in its own history.