A quick search for information on the No Fappers leads to No Fap September, an annual challenge to abstain from masturbation (but not sex) that is rumored to have started on 4chan in August 2009. This has, apparently, extended into an entire movement, and spawned an entire Reddit thread of its own.
Those entrenched in this fad preach some pretty serious benefits: from guaranteeing that those abstaining will get laid, to promises of better focus, clarity, and more motivation to take risks. While those are, of course, a big draw to the average young man who wants to try a new tactic for upping his game, those aren't the only folks who are drawn to (if not self-proclaimed pioneers of) the movement.
Lizzy Plaugic, of Nerve.com, recently wrote an article talking with some committed members of the No Fap movement that explored some of their personal motivations. It seemed notably strange that during this conversation about abstaining from regular masturbation there seems to be little to no discussion of male chastity, which has been a practice as a part of BDSM for far longer than No Fap's existence.
While there are some major differences between male chastity and the No Fap movement, they have enough in common that the absence of conversation about male chastity seems strange. While at their core, No Fappers and male chastity fans may have different motivations, submissives who have played with long term chastity have much more experience with the benefits of not jerking off on a regular basis
Chastity does still require some degree of managing one's own desires, but it also takes self-control out of the equation. Chastity lovers don't just receive the alleged benefits of abstinence, but they also benefit from knowing that they don't have to (and won't be able to) entirely choose when their release is coming their way. Rather than focusing on the community of other people who are not masturbating, though, long term chastity lovers seem content to hand over the power dynamics and deal with the results either within their relationship or on their own time.
Perhaps the crux of the differences between these two schools of partially abstinent men is this: The No Fap movement seems to largely be about self-improvement and community, as opposed to the pursuit of a sexual proclivity. In a time where young folks are constantly fed messages about a hook-up culture that essentially doesn't exist outside of college campuses and where the norms of sexuality and gender presentation are being increasingly re-evaluated and re-established, perhaps young men are turning to the No Fap movement as a self-imposed education in managing sexual desire.