There was the SS (Schutzstaffel) and the Heer (the Wehrmacht being the overall concentration of the military forces, excluding the SS). The SS carried out a majority of the killings in the concentration camps and in the field. The Heer was the regular army. They did not carry out many killings, but some units did participate, willingly or not.

But, what I think he meant by "different circumstances", is if they had met before the war (or without the war) they might have gotten a long as friends instead of trying to kill each other on the battlefield. After all, they were all young men and boys, regardless of their actions, and could have been very much a like. There are many instances of former enemies becoming "good friends" years after their respective wars. Probably mostly due to shared experiences and hardships, mutual respect and decline of hostility. But that is not always the case (most of the time I would think.)

Something I don't think you're thinking of or don't know about is, a lot of the people that participated in the execution of the Holocaust did not feel bad about what they were doing. They felt they were doing a good thing and doing their duty to their homeland and executing the will of their leader. They carried on like everyone else. They had wives, children, friends. They went to parties (in some instances, just yards from their victims at concentration camps), went on trips, listened to beautiful music, watched movies, etc. Just because you're a monster at work, doesn't mean you're a monster in your personal life, especially if you think (and are told) that what you're doing is the right thing to do.

It was Darrell "Shifty" Powers that mentioned that in Band of Brothers.

The reason that veterans say that sort of thing is, mostly, its true.

I don't have facts and figures to hand, but I would suggest that the percentage of German soldiers involved in death camps / genocide would actually be relatively low.

Imagine, you're a 18-20 year old lad, this war erupts and you feel its your duty to fight for your country, so you do.

On that level Allied and Axis soldiers were exactly the same. Transported miles from family, friends and everything they knew to see their new friends killed or injured, ending up in the most horrendous and scary situations you can think of.

Remember, not all Germans believed in Hitler and the Nazis and as war progressed and it became clear that Hitler was mad and that they'd lose the war many were trapped in this hell - and all for what ? They weren't all Nazi fanatics.

This is what Powers meant - some (many?) of the soldiers were just average guys that were in the wrong place and the wrong time. Had things been different they might have been born in the same town, gone to school together, become friends.