ADULT: public under adult content warning.
PRIVATE: not public
For instance, some guys dont want others to see their faces on this website for x reasons, most likely theyll put up landscapes or headless shots and keep their face pics under their private section to have more control of who can view his pics or not.
Some other guys might want to put up naked pics and they have no problems whatsoever to make them available to everyone, so instead they upload these shots under the adult section.
Sometimes you have a combination of these two cases, guys who put up headless pics on their profile but they also want to offer some x-rated headless shots under their adult section so they put their face pics under their private section.
These are just options you have available to use at will, most guys preffer to keep their naked pics under control, some others dont. You even find cases where some users put up headless adult shots under their adult pics and full body shots(adult) under their private pics. You only need to know the basic difference between adult and private(public under adult content warning and not public). How you use it is up to you, the option is there.
Finally the adult section gives the webmasters more control over new users who upload naked pics to their profile, obviously these users dont want to make their pics private but public and obviously these users didnt read the warning messages when uploading photos to this site. This way the webmaster does not need to take an aggressive decision by rejecting the pictures or by moving them to a non public section, they simply move them to the public adult section.
Hope this helps