The app says my store is online but I have pressed Pause here. Which one is right?

Both, and that is the catch. Pause on the app card stops orders reaching your kitchen: we refuse everything the app sends until you press it again. It does not close your store inside the app, so the app may keep showing you open and customers may keep trying. To go dark properly, close the store in the app's own tablet or portal as well. The Orders from delivery apps tab in the docs says this plainly under Pause.