Last question first Glen....the ADAHRS is a way of measuring attitude and air data - any EFIS has to has one, and it has nothing to do with how the data is displayed to the pilot.
A device which only wishes to display a velocity vector does not need an AHRS, and in fact uses completely different data.
An ADAHRS is an "Air Data Attitude Heading Reference System". If you don't display Airspeed, or Altitude, you are just an AHRS. If you don't do magnetic heading, you're an ARS.
The "A" inherently means attitude, but a velocity vector need know only two things, vertical speed and turn rate. Vertical speed and turn rate are not things that are displayed on a pure attitude display at all, so you can't just display one as the other. There are significantly less sensors needed to make a velocity vector display work than a full ARS. In fact, you can make a very functional velocity vector display with just a GPS.
In my biased words, this is how I would describe the difference:
An attitude display is what you are used to in every training aircraft you have flown. It shows where the nose of the airplane is pointed relative to the horizon. It works if you are stopped or upside down. If you are in a high AOA situation and have the nose above the horizon, but the aircraft is descending, it will show you as nose up.
A velocity vector display shows you where you are going, not where you are pointed. If you are upside down and not climbing or turning, it will show you level. If you are doing a flat turn with the rudder, it will show you banked. If you are in a stall with the nose above the horizon but descending, it will show you nose down. If you place it on the desk on it's side, it will show you level because you are not turning or changing altitude.
Some velocity vector displays do enhance their display with gyros, so that in the short term, they are showing you the angle of the aircraft relative to the horizon, but in the long term they are still showing you the motion. This gives them a more immediate response to the motions of the aircraft since a sudden change in angle does not always mean a sudden detectable change in something like vertical speed. This makes them much more useful in stabilizing an aircraft.
They are both functional displays, and in cruise, coordinated flight they often are indistinguishable, but in unusual attitudes and other situations they are vastly different, and a pilot using them should be aware of their differences since they are sometimes displayed in very similar manners which does not make it obvious what they are showing you.
As a side note, many full ADAHRS EFIS systems also display a velocity vector as an overlay to the standard attitude display.
--Ian Jordan
Dynon Avionics