It is quite obvious that there will be a slight bias based on which "camp" you are a member of. So I will do my best to remain objective here, but I am a member of the Soo Bahk Do/Tang Soo Do camp (although, those two camps are slowly growing further apart).
There is first, of course, the difference in the naming. That is quite obvious and has already been addressed.
Next, you have the difference in history. There are of course claims that various Korean martial arts trace their histories back thousands of years and are based on a variety of "ancient styles" including Tae Kyon, Subak, Hwarang, and others. For reality's sake though, based on the available
verifiable, unbiased, and objective history, the styles of martial arts practiced in Korea today trace their roots back to the end of the Japanese occupation. I realize that this topic can set off a thread of its own and many people are very passionate about the age and history of their style, but I think that we can all agree that during the Japanese occupation, a great deal of Korean history and hard documentation was lost, so following the occupation, the basically started over using what was remembered and hidden. The major historical difference was that when the original 9 Kwans united, under the umbrella, the Moo Duk Kwan (Tang Soo Do, Hwa Soo Do, Soo Bahk Do at different times) did not unite with them. There was at least one other kwan which did not unite, although I have heard conflicting stories as to whether it was Jido Kwan or Song Moo Kwan, both of which have since joined the Tae Kwon Do umbrella. The Moo Duk Kwan, to the best of my knowledge is the only of those original 9 Kwans who are still surviving today under their original set up and naming. Of course, there are division under Tae Kwon Do who maintain their original Kwan name as well. The Moo Duk Kwan is also still run and maintained by the Hwang Family (Hwang Kee passed it along to his son, H.C. Hwang).
Last, of course is the difference in style. There is a big problem here though. Across Tang Soo Do and Tae Kwon Do alike, there is a HUGE difference in styles. In fact, there are styles of TSD which are almost inditinguishable from certain styles of TKD and vice versa (aside from Hyung).
There is of course, the "sport" aspect of TKD which TSD really doesn't have much of. There are tournaments in TSD, but none of the level of the olympic style sparring found in some TKD schools. Not all TKD is sport based though, there are certainly styles of TKD which are much more traditional. In my observation, there does seem to be more Japanese and Chinese influence in TSD, the chinese side particularly in Soo Bahk Do. TKD seems to use much faster, lighter movements, intended to shorten the distance to the target. TSD seems to me to have much more use of the hips than most TKD that I have seen.
Another very minor difference is in naming - not of the art, but of the movements. I'm talking about Poomse vs Hyung; kong kyuk vs chirugi; etc.
To answer the question though......It depends.
Tell me which style specifically you're looking at, under which organization and we can get a lot more specific!