Self-hosted / Non-Custodial / Self-Custodial / Unhosted / External / Private / Crypto Wallet
A wallet is used to store virtual currency. Self-hosted (or 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.
The below list of terms all carry similar meanings but are used in different jurisdictions.
Check out these posts to learn more about self-hosted wallets;