Trust Wallet is a self custody wallet app, mainly for phones: the keys stay on the owner's device, and the coins stay recorded on their own networks rather than inside the app. It handles many coins and networks, TRC20 among them. Setting it up follows the usual steps: create the wallet, write the recovery phrase on paper, then pick a coin and network before receiving. Whether Trust Wallet is safe depends largely on its owner, through an official download, a locked phone and a phrase nobody else ever sees.
A bitcoin wallet on a phone suits small, frequent transfers, since the camera can scan the address code a casino cashier shows. The phone is also the weak point: it can be lost, stolen or infected, so a screen lock, current updates and a modest balance keep the risk within reason. A bitcoin wallet app belongs on the device only from the official store or the developer's own site, checked by the developer's name. Fake copies borrow known names and icons, and no app stays safe once its backup words have been typed somewhere else.
A USDT wallet is any wallet that supports USDT on the network being used, because USDT runs on several networks, among them TRC20 on TRON, ERC20 on Ethereum and BEP20 on BNB Smart Chain. A balance on one network does not move to another by itself. To create a USDT wallet, set up the app as usual, back up the words, then add USDT and choose the network before copying the address. Fees are paid in that network's coin: TRX on TRON, through energy and bandwidth or TRX burnt for them, ETH gas on Ethereum, BNB on the BNB chain.