Bitcoin Core is a full Bitcoin client and builds the backbone of the network. It offers high levels of security, privacy, and stability. However, it has fewer features and it takes a lot of space bitcoin core wallet setup memory.
This wallet gives you full control over your bitcoins. This means no third party can freeze or lose your funds. You are however still responsible for securing and backing up your wallet. This wallet is a full node that validates and relays transactions on the Bitcoin network. This means no trust in a third party is required when verifying payments.