An automatic, such as the familiar Allison, is a torque converter type tranny, very similar to an automatic in a car. It is built up and made much more durable for truck use, but it works on the car principles. Basically put it in drive and go.
Eaton and Meritor have what are auto-shifts. These are heavy duty truck trannies that do not have torque converters, and still must be clutched to get going out of 1st. From there, the Eaton one will up and down shift through its gears much like a standard automatic, or can be up and down shifted with the push of a button. The Meritor job does not shift automatically, but one uses the push buttons and does not have to clutch to make the shifts. These trannies are built internally like a regular manual gearbox, and use a computer to sense when the input and output shafts are in sync, then a mechanical actuator makes the shifts perfectly every time.
For lighter duty class 6/7 trucks the Allison is fine, anything bigger I'd go with the more rugged auto-shifts.
Those are the three I'm familiar with, there may be some others.
-Weave-