On Spot, while both providing the exact same market data (order books, trading history, etc.) and the exact same account data (account balances, order/trade status, etc.), REST and WebSocket do so in significantly different ways.
REST offers a call/response (question/answer) type interface and provides a snapshot of the current data, while WebSocket offers a live streaming type interface and provides real time updates.
An analogy would be the difference between a photograph and a video, in that upon request a photograph provides a snapshot of the subject but no further updates, while a video provides a real time view of the subject with live streaming updates.