Turnips are brassicas - related to cabbages, with an enlarged root that is cooked. The have a white skin, and are often grown as winter feed for sheep. A turnip can be very large, up to 60 cms in length and up to 100 cms around./
The radish is also a brassica; it is not cooked, but eaten raw for its strong and peppery taste. It has red, white or black skin. Most are quite small, apart from the black radish which can be long.
These photographs show the difference in size quite well: Google Image Result for http://img2.photographersdirect.com/img/21621/wm/pd1370130.jpg