As in the page nekojita-san linked, 玉子 refers to bird's eggs as a food such like hen's eggs or quail's eggs, whereas 卵 is eggs in general. Thus, 鶏の卵 is valid but 恐竜の玉子の化石 is not. (I remember my wife proudly asked if I knew the difference between 卵 and 玉子 just the other day. She seemed to gain the knowledge from a TV show or something.)