Exhibitionism is defined as the act of exposing one's genitals to an unsuspecting stranger for the purposes of sexual gratification. That is, you get off on exposing yourself. There is not necessarily any desire for physical contact, with many exhibitionists just showing themselves off, though some do include masturbation in the deal. Other kinds of exhibitionism less strictly defined include things like going to sex clubs, wearing extremely revealing clothing, or sharing homemade pornography with the internet.
A nudist, in contrast, is simply someone who prefers to not wear clothes. There is no sexual driving factor; for example, if one person in a flat of five prefers to walk around naked while the others do not, that does not make them an exhibitionist. They are displaying naturist tendencies, not being propelled by a need to get off.
This distinction is important, but it seems as though few people actually know enough to make it. Look at nudist dating sites, for instance. As with any online dating service, they are populated with a good number of creeps, but with the added downside of many people confusing nudism and exhibitionism. So if you do intend to use one of these sites, you will need to be prepared to block, block, report, block, and block again as you weed out the creeps and weirdoes.
That is not to day that there are no true naturists on these websites – that is who they were created for, and they are there. They'll probably be significantly less sexual than the exhibitionist creeps just trying to send dick pics to every one they can, which is a fairly simple test. An exhibitionist will send a dick pic; a naturist will just have naked pictures, not focusing on their genitals.
So a nudist is someone who enjoys a lifestyle of being nude, not motivated by sex, and an exhibitionist is someone who gets off on flashing other people, exposing themselves, and making people uncomfortable. And, believe it or not, there are true nudists on nudist dating sites like NudistDatingSites.net; you just have to be willing to put in the work to find them.