Non-Custodial / Self-Custodial / Unhosted / External / Private Wallet
A wallet is used to store virtual currency. Non-custodial means the owner of the wallet has complete control over the wallet as they have the private key. The key is needed to conduct transfers.
A custodial wallet is the opposite. The wallet owner does not have access to the key, the VASP does.
Check out these posts to learn more about unhosted wallets;