A workbook is saved into the project, the same way a Paper layout or a report is, so anyone on the project opens the same sheet you left.
The Save button
The Save button in the toolbar says which of four things is true:
Saved ✓: nothing to save. The button is disabled.
Save, with a dot beside it: there is unsaved work. Click it to save immediately.
Saving…: a save is in progress.
Retry: the last save failed. Click it to send again.
Hover the button to see how long ago the workbook last saved to the project.
Automatic saving
Spreadsheet saves on its own as you work, roughly once a minute whenever there is something to save. It also saves on the way out, such as closing the tab or navigating away from the project. Click Save at any point to save sooner than that.
Working with a teammate
Opening the workbook reads whichever copy is newest: your own unsaved local work, or a teammate's save, whichever came later. If you and a teammate are both editing at the same time, whoever saves last is the version that lands in the project.
What is actually stored
Formulas, number formats, colours, borders, charts and column layout are saved. The computed values are not, since they recompute from the formulas the moment the workbook opens.
The Usages, Features and Blocks sheets are rebuilt fresh from the live project every time the workbook opens, rather than saved as a copy. You can still edit the Usages sheet and push your changes back to the project.