Keys are how you receive and send your Bitcoin. (Public key is used to derive new addresses, private keys are used to "sign" a transaction.)

Coins, also known as UTXOs are chunks of Bitcoin (think like dollar bills for $USD)

Wallet (also known as a signing device) is what stores and uses your private key to sign transactions and it also uses your public key to generate new addresses associated with your private key.

Bitcoins are multiple UTXOs or coins.

I hope this helps.