They mean the same thing. One is Korean and one is Japanese. Dogi are usually wrap around style for karate. In traditional karate they are usually all white but some okinawan and kobudo systems wear black as do some American Kempo. Korean Karate (Tang Soo Do) often have colored lapels on a white dobok but still the wrap around style common in karate. Taekwondo Dobok can be V-neck, Y-neck, or wrap around. WT TKD typically wear a v-neck pullover but will sometimes wear wrap around similar to Karate during training. For Sport, WT has a specific poomsae (Korean for kata) dobok that is a wrap around that ties higher up near the ribs referred to as a y-neck. ITF/Chang Hon TK-D wear a Y-neck dobok. This one opens up like a wrap around but connects down the middle so the lapel forms a 'Y' shape. Hapkido dobok are typically wrap around and come in a plethora of designs and colors but they are usually distinguished from other styles by the diamond pattern sewn into the fabric. In Judo, the dogi is most commonly white or blue, although there are sometimes other colors used, and they are much heavier and tend to have reinforced stitching on the seams, extra fabric for padding on impact areas, and a much thicker lapel.
