A wallet is a combination of software (app or website) and sometimes hardware that stores your private keys to your crypto currency and other assets like NFTs.
The software can exist as a plugin in your web browser (MetaMask), an app on your phone (MetaMask, Exodus, Zelcore, Ledger Live, and others), as a stand alone application on your computer (Exodus, Zelcore, Ledger Live, Trezor Suite), or as a exchange/web site such as FTX.US, Coinbase, or Gemini.
A hardware wallet (Ledger, Trezor, Others) will work in conjunction with software to further secure your crypto and assets as the private keys are stored on the hardware device and you can only use them with the device connected and authorized.
In simple terms, think of a wallet as a safe deposit box that stores the keys to what you own on a blockchain.
You will have 1 or more wallets per blockchain platform you are using. You may have 1 wallet for Bitcoin, and another for Ethereum. They can exist in the same software, and hardware. but each will have a unique address that will only work on its platform.
Your wallet can also exists in multiple places, it can be on your phone in MetaMask as well as on your computer in the MetaMask browser extension.
No crypto or asset is stored in the actual wallet, the keys to gain access to the crypto or asset are what is stored in the wallet. However the software will usually show you crypto balances.
NEVER Share your seed phrase with a third party.