What a wallet actually does
A wallet manages the keys used to interact with assets recorded on a blockchain. The assets are not stored as files inside the app; the record remains on the network.
Public key and address
Addresses identify destinations within a network. They are derived from cryptographic mechanisms related to keys, although each blockchain can use different formats.
Private key
A private key can authorize certain actions. It must be protected because whoever controls it may be able to sign interactions associated with the wallet.
Custody and self-custody
In a custodial model, a provider manages the keys. With self-custody, the user retains control of their credentials. Each model involves different responsibilities.