Theres a good page on jindojunkie about the dosa.
The Name
The first thing to clarify is that "dosa" and "tosa" are the same word in Korean and mean the same thing to Koreans. The divergence in spelling is due to how the word is Romanized to English.
In Korean, the dog's name is

. The Romanization of

directly into English is "dosa," which takes into account of another Korean consonant with a stronger d/t sound.
However, since the dogs are mostly from Japan and the Japanese prefer "tosa" in their Romanization, "tosa" is more commonly used in the English-speaking world.
"Dtosa" will be used in the remainder of this page to re-emphasize that the two words are the same.
Are there differences between a Korean dtosa and a Japanese dtosa?
It's been generalized that the dtosa of Korea is this massively wrinkled, red beast while the dtosa of Japan is this fit and trim fighting animal.
This isn't quite true. In both countries, you'll see dogs of both types.
The dtosas in South Korea have their origins from Japan, and, as much as I would prefer it to not be, there are some Koreans who fight their dtosas. With similar origins and functions, many of these fighting dogs in Korea look very much like their fighting counterparts in Japan.
The majority of the dtosas in Japan are utilized for fighting, but there are reports where a few areas (Kochi, I think?) that have red dogs with wrinkles, similar to those in Korea, which caters to tourists.
A better way to catagorized the dtosa would be by type rather than from country. Koreans have labelled the heavily wrinkled, deep red dtosas as "Mee-Kyun", which translates into "beauty dog" and the fighting dtosas as "Thoo-Kyun", which translates into "fighting dog."

Meekyun dosa
Thookyun dosa