A draft event isn't yet publicly visible. Publishing makes the event live so people can book.
Save draft: keeps your work private; you can keep editing.
Publish: makes the event live. Bix checks you've set a title, date, location (or meeting link) and capacity first. An event using a seat map can only be published once its chart is published, and an online event needs a valid meeting link.
Visibility - a published event can be Public (shown on your site and searchable) or Private (unlisted; only people with the link can find it).
Unpublish: you can take a live event back to draft at any time from Manage Event. Existing bookings are unaffected; new bookings pause until you publish again.