Digital asset custody is a broader name for crypto custody: the holding and protection of cryptoassets, and the private keys that control them, by a firm acting for its clients. The main entry explains custody models, key management and regulation.
Banks, asset managers and regulators often prefer "digital asset" because the service can cover more than cryptocurrencies, including stablecoins, tokenised securities, tokenised funds and other assets recorded on blockchains. A firm offering the service is often called a digital asset custodian. Custodians typically combine cold storage for most assets with hot wallets for liquidity, and use techniques such as multi-signature or multi-party computation to protect keys.
Digital asset custody differs from self-custody, where the owner holds their own keys in a non-custodial wallet. In many jurisdictions it is a licensed activity, and rules on segregating client assets aim to protect them if the custodian fails.