First off, a tattoo is something that is a permanent mark where ink is deposited under the skin surface. Henna is form of body painting that makes a dark stain that penetrates deeply into the outer layer of the skin. That's your basic difference. Having something temporary is a good way to try out a design before committing to having it for the rest of your life.
How long they last can vary from person to person. The recipe of henna paste ingredients, how long you leave the paste on your skin, how warm the environment was when it was painted and where on your body it is done all contribute. Designs can last from anywhere from one to about six weeks.
Please note, if you get a henna body painting and don't like it, you cannot wash it off. You must wait for the stained skin layer to grow out and be shed.
I've got a little eBook on Henna, with instructions on how to do this at home yourself. http://www.bellaonline.com/ebooks/ebook41