Unlike regular kombucha, which is fermented with cane sugar and black tea, Jun is made with green tea and relies on a honey sweetener. It's more mild and less sour than traditional kombucha as a result.
The main difference between Jun and kombucha is that the SCOBY (acronym for symbiotic culture of bacteria and yeast) is trained to feed off of honey rather than sugar from the start. If you put a kombucha culture in a honeyed tea, the bacteria wouldn't feed properly and would likely die. The Jun culture, however, is designed to use honey as its fuel source.