BTC and sats name the same asset
A satoshi is not a separate token. It is a smaller way to count bitcoin, just as cents are a smaller way to count dollars. Wallets may let you switch the display between BTC and sats without changing what the wallet controls.
The name honors Bitcoin’s pseudonymous creator, Satoshi Nakamoto. The plural is usually written as “sats.” A person can receive and spend a fraction of one bitcoin; owning a whole coin is not required.