Trust Wallet is a mobile wallet for Android and iOS devices that supports Ethereum and over 20,000 different Ethereum based tokens (ERC20, ERC223 and ERC721). Trust Wallet also has a desktop version (beta) that supports Windows, Mac and Linux.
Coinbase is a digital asset exchange company headquartered in San Francisco, California. They broker exchanges of Bitcoin, Bitcoin Cash, Ethereum, Ethereum Classic, Litecoin, Tezos, and many others, with fiat currencies in approximately 32 countries.
You cannot directly use Trust Wallet with Coinbase. However, you can use Trust Wallet to store your cryptocurrencies that you purchase on Coinbase.
For example, if you buy Ethereum on Coinbase, you can store it in your Trust Wallet.