Some people use these two terms interchangeably, others consider there is a difference. The difference claimed is that naturists have a greater interest in connecting with nature through their nakedness.
A stronger difference is geographical. The US tend to favour the term Nudist whilst in the UK the term Naturust is more common.
My own opinion is that to be a nudist all you have to do is be nude and that could be for any reason, whereas the term Naturist describes someone who is comfortable with non-sexual social nudity.
it's in the word. Nudists go straight up nude for the f*ck of it (or whatever crazy protest they're joining), and naturists go nude in protest for the inhuman treatment of wildlife that overly benefits modern society.