Well, the first is simply an A7V under construction I guess. You can see how crude the lavette was. And the second, yes, a trench digger. That one I haven't seen before. Interesting!
But we have people here that are more experts than I am. Hopefully they can illuminate us even further!
That photo of the A7V trench digger is in Hundelby and Strasheim's book, as well as two other photos of it. It used a shortened chassis with only two bogies per side instead of three. It looks like the wooden driver's cab overhangs the tracks quite a bit in the front.
The first picture is the A7V 506 under repair at the BAKP 20 located in Charleroi, during March 1918. Which shows its 5.7cm Belgian Nordenfelt gun with a buck mount slide back, and its Armour removed for repairs, A7V 501 is next to it.
The second picture is an A7V Baggergraben?? {Excavator trench digger}, this is the name I have been given during my research, I am not 100% on that as of yet. The vehicle had a shortened chassis from an A7V Uberland-Galandewagen, Its track system only had 2 bogie wheel sets instead of the normal 3 found on the standard A7V chassis, Also the cab resembled a Large lorry type of the period, being constructed out of wood and metal, The engine was a single Daimler type 165-204 engine, used by the A7V’s, which was relocated to the front as a standard vehicle would be arranged. It carried a very large trench digging device in the rear on the vehicle, capable of removing earth to a depth of some 2.5meters, {8feet} and jettison it on either side of the trench by two special conveyer type devices, to which the earth would me used as a rampart. The excavator devices were powered by an additional Daimler motor housed in the center of the vehicle. Some sources say 20, some say more chassis were converted to make these vehicles, I am not sure, But I would welcome any more information.
Wow, I didn't know that there was a second photo of the Schutzengrabenbagger! But from the other photo i've seen, I'm convinced that there were two built, but one was damaged in the field.