Many of the earlier first ascents, particularly for difficult routes, involved a mix of free and aid climbing. As a result, purist free climbers also identify a first free ascent (FFA), made using equipment for protection only and thus more challenging.
First ascents, free or otherwise, are generally carefully recorded as part of the history of a mountain or climbing area, and usually mentioned in guidebooks. Some area guidebooks consciously choose to omit this information, so as to discourage disputes over priority and excessive bolting of faces so as to be able to add up new "first ascents".
Wags also use the term "last ascent" to refer to a climb that is so unpleasant or unaesthetic (due to loose rock, excessive brush, etc) that no one would ever willingly repeat the first ascent party's ordeal.