Ha, I asked because I thought there might be some kind of carryover but, yeah, I got nothing.
Long story short: I started off studying and teaching martial arts, then got certified as a trainer (ISSA CFT). Trained clients at the dojo and in a few gyms. Eventually dropped the gyms and found clients on my own, usually training in their homes, and started doing more online consulting. Now pretty much only do online work with clients.
The last few years, I did begin to specialize on working with, believe it or not, paintball players. When I started, because of my background, I thought I'd end up the next big MMA strength and conditioning coach. That didn't happen and I'm 100% fine with that.
It's a fine line, but "technically" certified trainers aren't "supposed to" dispense strict nutrition plans unless they have specialized nutrition education. I give guidelines, of course, because diet and training are so complementary, but I usually clarify that it's "I'd focus on this and that if it was me"-type stuff.
For sure some people get certified and do both. One some level it's about what you want to invest in getting "the paperwork" and what it'll bring you in the longterm. I began studying both ISSA's youth fitness training course and their specialist in martial arts conditioning, but didn't complete either for various reasons. I do still refer to the info/textbooks from time to time.