Whats a Camcorder??!

My mom is wanting a camcorder for xmas... I'm good when it comes to picking out a camera... but a camcorder? I am little lost. lol I've seen some what I think to be nice ones for around $300-400 marked down to $160.. which is our price range. I want a good brand like Canon, JVC, sharp, sony... no off brands. I know I want at least 30-40 optical zoom, good battery life, good video quality that I can watch on my t.v and it not look bad, good sound too... but i'm not sure what to look for on that stuff... also what's better, recording on a SD card or directly to a DVD?
i've heard some say SD but others say they like the straight to DVD.. or maybe get one that does it both? do anyone know whats a good one to get? it's for family events and just mostly family and friend videos so i want the good quality.

what kind of camcorder do have you?