There were three different types of camps.
Concentration Camps where not only Jews, but political opponents and union organizers, Catholic Priests who objected, Communists, Socialists, Social Democrats, Roma, Jehovah's Witnesses, homosexuals, and other undesirables or persons accused of 'asocial' or socially 'deviant' behavior were held.
People were poorly treated and many did die due to deliberate maltreatment, disease, starvation, and overwork, and some being executed as "unfit for labour" and from 1941 to 1943 there were active euthanasia programs (14f13) in these camps to remove those considered to be unable to work for "health reasons," however this did include the "ailments" of being Jewish, handicapped, or having criminal or antisocial records
In 1943 two things happened
Factory Slave Camps were formed and those considered able to work for those were transported out of the Concentration Camps to those, where many were literally worked to death
Secondly the Extermination Camps were opened, and the death programs were stopped in the Concentration Camps, with those being regarded as needing to be eliminated, starting to be sent to those instead. That didn't mean that those left in the Concentrations Camps were treated any better, and nor does it mean that those suffering in them weren't dying due to malicious treatment, rather that they were no longer being killed at them as part of the extermination program. In fact a number of the camps were switched to using the populations for inhumane medical experiments instead of outright killing the occupants, which could be considered worse in some ways. many POWs, especially those from Communist Russia, were also send to these camps later in the War.
Nearly half of the Jews killed in the holocaust died in Concentration Camps rather than being sent to an Extermination Camp.
Something else to note. While the Jews were the largest group of those killed, collectively they were only about 35% of those exterminated with around 11 million non-Jews, primarily Soviet citizens and POWs, but also including Serbs, Poles, the disabled, Roma, Jehovah's Witnesses, those deemed to be Criminals, Homosexuals, political opponents, and blacks, also being murdered in the camps.
I have to agree with the USHM that we shouldn't refer to the detention centers as "Concentration Camps," however, if we did want to go with a Historical reference from WW2, then perhaps "Internment Camp" might be a better one.