Best photos are under a white light, but I can see what you are referring to.
One looks like an injury, the other more of an infection. Ideally they are in a QT for treatment. However if already in the main display tank, Kanaplex is a good/mild antibacterial treatment. Be sure they aren't fighting with each other or that any other tank inhabitants are fighting with them.
Online purchases can be somewhat of a gamble. There are reputable online sources which
actually do a proper quarantine of their fish before shipment. I would only buy from one of them, if online is your preferred source.
If the Kanaplex treatment doesn't seem to help, I'd move the fish into a hospital tank. Considering this, I'd get a hospital tank up and running right now, and have it ready.
Anthias in general are prone to Uronema infections in addition to having feeding requirements unlike most of the ornamental marine fishes.
Be sure to Download then read, the
Fish Nutrition document
