MGTOW consists of men who are abandoning the path prescribed to them by society and feminist agendas: the path that consists of training in their young lives, marrying in their late 20s, working and sacrificing throughout their lives for someone else's benefit, getting divorced, becoming estranged to their children, and eventually dying alone and with no real sense of what their lives were about.
MRA consists of men who are actively battling institutionalized and subrosa sexism in our legal and cultural dialogues - sexism which accommodates a lot of the exploitation and abuse described above, and which MGTOW try to avoid.
PUA consists of men who, either awakened or in the process of awakening, are learning how to get the sex they need without paying the price demanded to them by a media and culture that has women's interests mainly at heart. It's a community about learning the fundamental principles of what makes a man attractive to women, how to become that kind of man, and a methodical guideline of the various stages of attraction and seduction, culminating in sex.
Personally, I think the three groups need to be communicating a lot more than they are.
Simple, direct, easy to remember. I think he nailed it. The only thing I would add is that PUAs are a subset of MGTOW since they're both groups of men who reject the social expectations to "man up" by doing what's best for women (the feminine imperative). Also, of the MGTOW who don't chase tail, those men are referred to as "going ghost", or "going Galt" in reference to Atlas Shrugged.
Overall all three camps fall under a larger umbrella of the Men's Movement, of which this blog is a part of. Additionally, all three camps can be thought of as being Red Pill savvy. Online many would refer to Red Pill related blogs as the "manosphere".
Lastly, I completely agree with his/her's last comment, that we should all be working together and communicating in a more productive manner. We're still a long way off until the misandry bubble bursts, and working at cross-purposes can really hamstring our progress.