- a private key or set of private keys which are used to sign transactions - hardware wallets store this inside the "hardware wallet" thing
- a program that interacts with the Bitcoin/Ethereum network, can display balances on a (public) key or make transactions that need to be signed by a private key (those are different, you'd use e.g. Electrum for Bitcoin and Metamask for Ethereum)
Obviously both of these can be the same (you can store your private key in a file accessed by Electrum), but to reduce the probability of getting hackes people often separate the private keys from their wallet programs.
A coin-denominated account on an exchange is often also called a wallet, but it's just an account on the exchange like you'd have one in your bank.
Just go to Trezor’s home page and read. It’s the best wallet for most people, and they make money just like any other seller of wallets in a store.