When you share the proof with another person via the Share Menu, that user will receive an email notification inviting them to the review with any custom message you include.
When you @mention another person in a comment, that user will also receive an email notification that includes the comment, inviting them to the proof if they are not already an active reviewer. If they are an active reviewer that has not yet submitted an approval status, they will then be required to do so. If they have already submitted an approval status, they will need to resubmit their status.
If you invite new reviewers to the proof they will receive an email requiring them to review the proof and submit an approval status. The user will also receive an in-app notification. The proof owner will receive an email notification each time a new user is invited to review the proof.