I'm not sure there is a difference, I've always thought they were interchangeable terms. But I could be wrong so I'm anxious to see what others say.
I think they mean the same thing but with different connotations. You get nudists going to a nude resort or a nudist beach.. You get naturists wandering around their gardens without clothes, or in quiet places in nature which are not specifically for the purpose. People who get a kick out of the excitement of it, or of people seeing them, I would call a nudist. Someone who does it because it feels normal and natural is a naturist.
I am a nudist, I sleep, work, eat and play naked. I take vacations where I can be naked and my favourite places to vacation are in the mountains in Alberta and B.C..I find nothing more enjoyable than being naked on the trails and in the streams. Being naked in the natural beauty of the mountains gives me great peace of mind. There is nothing more freeing than being naked in nature. I understand where the term naturist comes from.
Nothing. Naturism is a more polite term in conservative circles. They think you're talking about Prof David Rabbitburrow... aw for shame, I've forgotten his name... the naturist guy? Naturalist.