As a beekeeper, wax moths are an arch enemy. I have lost more frames of bee hives to them than I care to remember. Wax moths, in NY, are about 3/4 inch gray to white and do not show up until mid summer. Probably 60 degree nights might be their minimum. Wickapedia would be good idea.
No they do not eat the nice clean bees wax. They lay egs and the larvae tunnel around through the dark cocoon filled brood areas wax in unused, stored hives. They like dark, Sunlight keeps them out of the hive but let's bees in.