For more about the differences between soju and shochu and how a couple of independent soju brands are being produced, see Soju and Shochu: Cousins in Craft Distilling.
One of the most important distinctions between soju and shochu is the difference in fermentation starters—it’s nuruk for soju, and for shochu it’s koji.
Nuruk is a mixed culture cultivated from grains and local air, and it typically includes yeast and bacteria as well as the Aspergillus oryzae mold whose enzymes aid saccharification. Koji, on the other hand, refers to the mold itself (though the word can also be used for grains that have been inoculated with it, especially if used as a starter).