Saved PGN games: Up to 1,000 per account, with no time limit. Saving the 1,001st removes the oldest.
Notes: The limit is 1,000 games, not 1,000 notes. Each annotated game counts once, however many moves you comment on. No time limit. Annotating a 1,001st game deletes the notes of the oldest one.
Signed in vs. guest: Signed in, both are saved in the cloud with your account, and you see them on every device until you delete the account. As a guest, they are stored only in your browser on this one device. They never reach your other devices, and clearing the browser's data deletes them. Create a new account here and your notes move to it.