Custodial Wallet - In a custodial wallet, a centralized body holds on to the “custody” of your digital assets for you. Custodial wallets tend to be more user friendly. The Switch Trade Wallet is a custodial wallet.
Non-Custodial - In a non-custodial wallet the user has full control of the private keys(seed phrase and encryption passcode). No third party approval is needed to send funds from this wallet. The encryption password is important as it is required to send assets out of this wallet. It is the user's approval of the transfer or transaction giving them that full control of the wallet and the assets. A Switch Reward Wallet is a "non-custodial" wallet or "decentralized" wallet.