Both AutoPushes and PushLetters are push notifications, with slightly different characteristics:

An AutoPush is an automated, scheduled message set to go out at a timed interval. You can schedule from 0 to 90 days worth of automated notifications.

PushLetter is a 'blast' aka a one time broadcast to your list of subscribers.

These are similar to the traditional email autoresponder services wherein autoresponders and broadcasts/newsletters are AutoPushes and Pushletters respectively.