The reactions of the front-line troops that first encountered the camps were pretty universal: horror, pity, and compassion. Soviet, British, or American, the grunts who encountered the camps pretty much universally gave the prisoners food, clothing, whatever they could (often with tragic results - the starving prisoners would gorge, and their systems couldn't handle it).

Generally speaking, the West took more care of the prisoners they found. The Western Allies would document them, rehabilitate them, organized camps to house them, etc. The Allies weren't stupid, and knew that there would be a massive refugee problem; they set up the United Nations Relief and Rehabilitation Agency to come in behind the armies and care for and repatriate the refugees.

The Soviets (who liberated the vast majority of the camps) gave much less help. UNRRA was not active along the eastern front, and in general the Soviets disavowed there being any refugee problem at all. The usual sequence of events would be Red Army troops arrive at a camp, say "you're free now!", and then move on. Some survivors who needed care ended up in hospitals, but to a large degree they were left to their own devices.

There's plenty of great books that deal with this stuff. Waiting for Hope by Angelika Konigseder and Juliane Wetzel is one I would recommend.

I can't speak for the Soviets, but in the West concentration camp victims were generally kept together. They were moved to better accommodations as soon as was possible, but keeping track of them in an organized manner so that they could be taken care of, and possibly be reunited with family members, was important. They were not necessarily held against their will or anything, and indeed many were deeply suspicious of the Americans, particularly in terms of medical care., so much so that they left. The system for supporting these survivors was not perfect by any means either.