Although the word "virgin" is neutral (and silent) on the question of volition, due to the medieval mores and mannerisms which continue to linger within society, the word virginity gives off harbingers of volition, intentionality and willful sexlessness due to the Virgin Mary story. The Virgin Mary story has ingrained virtue and honourability to the notion of sexual abstinence. As such, it has become difficult for many people in the western world to understand the concept of the sex deficit, which has become so profound, it is even affecting normie-tier men.
Nutshell: In a nutshell, comparing virgins with incels and assuming they're the same thing is equivalent to saying that a starving child in an Ethiopia famine is the same as a middle class guy who is on a diet. Technically they're going through the same thing (i.e. avoiding food), but other than that, they have little in common.