春卷 (Chūnjuǎn, Spring rolls) are julienned vegetables, sometimes with a bit of noodles, sometimes with a bit of minced meat, wrapped with a flour dough skin and pan- or deep-fried. They are a filled roll.
You can see the different varieties by country here: http://en.wikipedia.org/wiki/Spring_roll
鸡蛋卷 (Jīdàn juǎn, Egg rolls) are many different things around the world. In Chinese communities, these typically refer to a sweet biscuit type roll, of hollow flaky egg pastry (not filled.) However, there is also another variety (common in American Chinese cuisine) where a flour dough wrap is filled with "pork, shrimp, or chicken, adding cabbage, carrots, bean sprouts and other vegetables, and then deep fried." In the American Chinese respect, I believe it is very similar to a Spring roll really, although the flour dough looks thicker and of a different composition than a typical Spring roll (the dough bubbles when deep-fried, with Spring roll skin it does not.)
Sweet egg roll:
American Chinese egg roll: