@Olivier5,
Just to get the (German) names correct - and that's only (!) for the concentration camps between 1933 and 1945:
the German name is
Konzentrationslager (short: KZ), which was a literal translation of the English term "concentration camp".
There were roughly 1,000 of those camps, including sub-camps.
The seven "extermination camps" (German:
Vernichtungslage) were concentration camps in Poland and Belarus, mainly erected only to systematically kill millions of people.
Concentration camps were youth detention centers, extermination camps, labor camps, transit camps, women's camps and other concentration camp-like units (e.g. secret police's camps, SS-camps ...)
The first KZ was built in Dachau in 1933, for political prisoners.
The death rate in the 1,000 camps (excluded the seven extermination camps) was about one third of those imprisoned.