No, they are different. Holly is a green plant with red berries, and a traditional symbol of Christmas, I'm not sure why. I actually thought we had a holly wreath hanging over our door right now, but I see it is really some kind of pine. Holly really is a common Christmas decoration.
Mistletoe has white berries, and you don't see it very often. People will hang a sprig of mistletoe over a doorway, and there is a tradition that if a man "catches" a woman standing underneath the mistletoe he is allowed to kiss her. To tell the truth I've never actually seen this happen in real life. But then I've never been at an office party where people really got drunk, either.