Information on Korean Jeju and Korean Jindo dogs can be hard to find, so I am not sure how much of this is true, but I am sure that not all of it is false.
The Korean Jindo is a hunting dog whose origins can be traced to Jindo Island in South Korea; the Jeju dog is also a hunter, but it may have originated elsewhere (perhaps China) before being brought, thousands of years ago, to Jeju Island, where it became the military dog of choice.
With only minor differences, Jindo and Jeju dogs are similar in size, shape, color and demeanor.
When the Jeju dog fell out of favor with the military, it became the regional dog meat of choice, leading the breed to the brink of extinction in the 1980s, when only three Jeju dogs could be found on all of Jeju Island. It is my understanding that Jeju Island remains the leading source of dog meat for consumption in South Korea, where eating dogs is illegal but tolerated. There are now a few hundred Jeju dogs on the island, but less than 100 are known to be purebred.
I spotted three dogs on Jeju Island with characteristics of one or both breeds: