The second one is definitely a dendrobium. The first, tiny one, I'm not sure, but I think it is also a dendrobium.
As far as the roots on the tiny one go, they look fine to me. Pot it in some bark and give it a good watering, then leave it be until the medium is almost, but not completely dry. Someone with more experience with these large dendrobiums should chime in and give you a hand with how often to water.
The larger one though... I'm not sure. A lot of how you tell if a root is rotted or not, is in how the root feels. It will feel flat, or squishy. Healthy roots feel firm, sort of like a fresh green bean. The color, could be from rot, or it could be from the potting medium the plant was in. So, go ahead and feel up the roots on that second one. If you have a lot of flat roots, you are going to have to cut those back until you get to healthy plant tissue. I see some good roots on this plant though, so it's not a lost cause, but if the root damage is as extensive as it appears, it could take a while for this plant to recover.
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