The difference is very subtle, and the definitions likely differ from one nudist/naturist to the next. I consider myself to be a naturist rather than a nudist (and I'm in the US). I tend to think of nudists as seeing nudity as more of a social thing, something to be enjoyed with friends at home or at a nude beach/resort. Naturists see of nudity as a way of life, a healthy lifestyle that lives clothes-free and greatly appreciates the link between being nude, which is perfectly natural, and the rest of nature. I would also tend to think that while nudists don't mind wearing clothes in clothing-required situations and locations, naturists can't stand to wear clothes because they feel like an uncomfortable covering of the body, and can't wait to take the clothes back off. Of course this is all just my own subjective opinion.
In reality, nudists and naturists are very much the same.
naturist for 20+ years