Was there ever even a clear distinction between assault guns and tank destroyers? I don't know if they worked with pure infantry or mechanised/motorised infantry and if they were part of the artillery throughout the war or if they transitioned to the armoured corps later on.
Thanks for any answers to this question(s).
Yes, there was such a distinction between assault guns (Sturmgeschutzen) and tank destroyers (Panzerjagern)
Officially, StuG crews were part of the artillery branch and wore their waffenfarbe (branch color) which was red. By the end of the war, however, limits on the amount of tanks available resulted in the use of StuGs as ersatz tanks in Panzer units.
AT crews (e.g. Maders) are a more complicated. They were considered part of the branch of the regiment or battalion to which they were attached. So an AT unit attached to an regular infantry unit of those sizes would wear the white of infantry, or green for a Panzer Grenadier unit. An AT unit attached to the Panzer regiment would wear rose pink, the color of the tank troops. Divisional AT units were always considered to be Panzer arm, and always wore pink regardless of the nature of the division.
However, at the Corps or Army level, any independent AT battalions were considered artillery, the troops of these Artillerie-PaK-Abteilungen would wear the red of artillery. Similarly, there is a post over on Wehrmacht-awards.com stating that as Corps level assets, the crews of Sturmartillerie (Sturmpanzer, Sturmmosser) were considered Panzertruppen and wore pink.