Well, “nuclear” has come to mean “fission,” because that’s how it’s used in every nuclear energy system today. “Fusion” isn’t something that exists in a meaningful way outside of science labs.
So I think that association is fair. If you mean “fusion,” you should say “nuclear fusion.”
What exactly did you learn? If it’s that there are a number of different types of stem cells, then we really need to improve scientific communication to the average person. I learned this kind of thing because I’m interested, but I thought this was being taught to kids since they were an active area of research (something like 15-20 years?).