Chili powders are different. For one thing, the heat they produce can notably effect different areas of the mouth. Still, they are all chili peppers and many are hot and all are red, when ripe and dry. Also, there are sweet peppers, like paprika, that are not hot at all, or only very mildly, and these pack quite a flavor punch without heat, so it is not only about heat. There are many subtle and not so subtle differences.
I made my first Kimchi with mexi-style "California" chili, as they are labeled in this state. "California" chili is supposed to be mild. I also add some homegrown dried Fresno chilis and some other ground up hot chilis, which may have been what they label as "Japanese" chilis. I used a blend. At first I was disappointed with the flavor, but after the flavors had mingled after 24 and then 48 hours, I found the flavor of my Kimchi very much improved, quite hot, and more than satisfactory.
While personally I would really like to try some authentic Korean chili, if you are interested in making kimchi and can't get a hold of Korean chili or find it difficult, don't let it be and obstacle to making kimchi right now! Just use whatever you can get your hands on that suits your heat preference. Season to taste. I found myself using much less chili than my favorite recipe advised and my kimchi was still well seasoned and quite richly red hot. Kimchi, cabbage and salt is such a magical enzymatic, probiotic, herbal, medicinal product, that I advise you not to procrastinate but make some right now!
I also emptied a two super probiotic capsules into my kimchi to give it a headstart into lactic acid land and help avoid yeasty pitfalls, as well as make my kimchi more medicinally viable. But they magic with the cabbage and salt starts really early on in the culturing process. After just 45 minutes of soaking my washed cabbage in salt it tasted magically enzymatic. Every stage of kimchi has it's own virtues. By all means make kimchi with whatever ground chili you can get your hands on!