At risk of being pedantic, how did Rob Reiner's uncle manage to be part of the Normandy Invasion and to liberate "the death camps" ?
In all the serious historical writing about WW2 and the Holocaust I've read, the term "death camp" refers specifically to the extermination camps like Bełżec, Sobibór, and Treblinka. Some concentration camps, such as Auschwitz, Majdanek, and Jasenovac, had death camps attached, but concentration camps and death/extermination camps had different functions.
In concentration camps, the inmates were used as slave labour, being worked to death until either malnutrition, disease and maltreatment took their course or until they were judged unfit for work (or their captors simply needed to make room for new inmates) and transferred to the extermination camp part of the camp complex to be murdered.
Death camps had one single purpose -- the swift murder of entire populations, with the vast majority of the victims surviving no longer than a few hours after arrival. The only slave labourers there were inmates needed for the day-to-day running of the camp, who survived for a few months until the Nazis disposed of them, too.
These camps were either liquidated by the Nazis or liberated by the advancing Soviet forces.
The camps liberated by the allied forces, like Belsen, Dachau or Buchenwald, were concentration camps in Germany, Austria and (I think) Czechoslovakia. They were primarily labour and internment camps, where conditions were terrible, the regime brutal and murderous, and prisoners' life expectancy typically short, but they did not normally carry out mass executions -- when the SS wanted to do that (e.g. to make room for new inmates) the victims were typically transported to extermination camps further East to be murdered.
The horrifying conditions encountered by the Allies in the camps they liberated were primarily caused by the way the Nazis liquidated their concentration (i.e. slave labour) camps further east as the Soviet armies advanced. Since the prisoners were considered as resources to be exploited as part of the Reich's war effort, they were made to undertake dreadful forced marches back to Germany, where the survivors were dumped in the concentration camps while the Nazis tried to decide what to do with them. Disease and starvation followed as the Nazi state apparatus collapsed, since as the prisoners no longer had any value as slave labour, the Nazis had no interest in their further survival.