Admin keys (previously called Auth keys) are keys that have full authority of a contract-based account. Admin keys can add or remove other admin keys. Admin keys should be fully secured.
See Admin key.
Dapp keys (previously called Login keys) are ephemeral keys generated when logging in to dapps. Dapp keys can only be used for signing transactions. Dapp keys may have more restrictions to provide more security on questionable dapps. Dapp keys cannot add or remove admin keys.
See Dapp key.
A relayer is a service that attaches the gas fee for a transaction. The relayer is typically refunded by the original transaction signer. Some relayers accept the refund to be in a token instead of ETH.