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 internal history.
A bitcoin wallet address is a long run of letters and digits that usually starts with 1, 3 or bc1, depending on its type. Finding the address of a personal wallet means opening it and tapping Receive. Many wallets show a fresh bitcoin wallet address for each payment to protect privacy, and older ones keep working. The receive page also shows a square code the camera can scan, which avoids typing errors. A pasted address still deserves a second look, with characters at its start, middle and end compared against the original.
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 accepts.