No, I’ve found there are two distinct sub-categories of exhibitionist. Both like to be seen naked but in different ways.
The more obvious, but less common kind are the confident, happy to be seen naked type. They love to show off, will happily expose themselves and often describe themselves as nudist/naturist. These are the ones that most people know about. Everyone knows someone who ends up naked at parties, leads skinny dipping, streaks or volunteers for dares.
The other kind seems to be more numerous but much less visible. They love to be seen naked or in some way expose themselves but are shy about doing so. They usually will not volunteer to be naked and need a reason or justification to be naked. Being ordered to strip, losing a strip game or even pretending to be hypnotised or blackmailed are ways they give themselves licence to be seen naked. Often they love the intense humiliation of being naked in front of other people, although this is not always the case.
The first kind is a showoff or performer. The second tends to be submissive. Both get a thrill from being seen naked.
It would be great to gather proper statistics on this.