There are two types of addresses on the ethereum network: EOA addresses and contract addresses.
Casa Pay (EOA)
Your ETH Pay Key address is controlled by a public and private key pair. This key can send and receive funds, and interact with smart contracts.
The address of your ETH Pay wallet in the Casa app generates a single address that does not change. Unlike UTXOs, which need to generate a new address for each deposit, addresses on the Ethereum network are account based which is why there is a single address.
Vaults in your Casa app are contract addresses. Contract addresses are controlled by contract code. They run code every time an address interacts with them. This code can do a wide variety of things, from simply updating a balance to creating new digital assets.
In this case of Casa Vaults, the contract governs how many keys are necessary to sign a transaction and specifies which keys can sign transactions. If and when you need, you can replace a key that can sign transactions for your vault. When you replace a key, the old key is removed and replaced with the new one you specified. The contract code updates this after a quorum of signatures has been verified.