There are several different types of Sent Email in Matrix (My Matrix> Sent Email):
Publish means it was an autoemail set up on Concierge Mode that the user approved and sent on to the Contact.
Direct Email is a listing (or group of listings) that the user selected and manually emailed to the recipient.
Report means the user emailed a PDF report.
Auto Email shows up when a listing (or group of listings) was sent automatically.