Dave said an A minor chord starts on an E. I wasn't aware of that. Hence the different sound.
Well, that's only if you're strumming all six strings. You don't HAVE to. In fact, when I was just learning piano I started transcribing the notes from my guitar and I played my D chord with an E on the bottom! YIKES. What a noob I was. As I progress in my guitaring, I find myself using fewer notes. I'm really trying to make the notes count, instead of just filling up all the holes.