is living clothes free and being an exhibitionist the same?
There is no mention of compulsion or sexual satisfaction in either description of nudism, just as there is no mention of culture, a social activity, or lifestyle in exhibitionism.
Nudists and naturists don’t seek to shock people. Yes, they like to be naked, but that is for their personal good, not for others to stare at or be shocked by intentionally. They don’t want to ‘exhibit themselves’. That would be quite difficult considering that they would do that in a group that’s already naked. An exhibitionist wouldn’t stand much chance in a nudist setting. Any attempt to try something sexual in a nudist setting will usually be dealt with quickly.