I have heard some people claim to be naturists and not nudists for the same reasons that others claim to be nudists and not naturists. Same goes for "nude" vs. "naked." Consensus is difficult!
For myself, I consider them equivalent, and don't care which of the two people use to describe me. I use them both, but "naturist" more often for no particular reason. However, I also respect that people have deeply held beliefs about being one or the other, and if I know someone's preferred terminology, I will use it. If I don't, I will try to find out. If I get it wrong, I will apologize and use the other word.
Ultimately, I don't like labeling myself very much. I'm a person. There are other words that describe me, but they don't define me. Some people find labels very helpful; I find them constrictive. But, to each one's own!