"Identifying German or Soviet divisions." Topic

As I understand it, neither German nor Soviet standard infantry divisions wore division patches like the Allies did – (excluding certain elite German units who had cuff titles).

So if I am leading a patrol tasked with identifying the specific unit of the enemy in front of me, how was that done?
Was there anything besides prisoner interrogation, hoping they just adnit it?
Did they have ID cards or paybooks or anything with that type of information?

So suppose my squad gets in a firefight and drives off the enemy, they fall back leaving no living soldiers. Howw easy was it to figure out who they were?

I am thinking of a situation where there has been a breakthrough and there are no clear and coherant enemy lines – so they could be anyone.

The Germans would have their identify/pay books. See this link: link

Don't know about the Soviets.

Jim