There is no such thing as a wallet that contains your coins. Assets live on the ledger; a wallet holds the private key that authorizes moving them. Whoever knows the key is the account.
Keys, addresses, signatures
A private key is a very large random number. From it you derive a public address, and with it you sign transactions. The chain verifies the signature; it never asks who you are. Identity is reduced to sign(message, key).
Custody models
- Custodial: an exchange holds keys for you. Familiar UX, but you hold an IOU, not an asset.
- Self-custody: you hold the key, typically behind a seed phrase. Full control, full responsibility.
- Smart accounts: contract wallets with recovery, spending limits, and multi-signature policies.