Simply put, PT is less a terrorist organization and more of shadowy paramilitary entity that do the dirty work for *sough*saintly*cough* United Nations. Think
Titans from UC, but less of a monster, more like ruthless special force.
Most of the time, they are in-universe version of rocket trio. Totally inept and sometimes hilariously wacky (Madoka, that means YOU). When they
are serious however, something is screwed on a large scale, be it a mega corporation or a whole country, or alien battle-fleet. Basically anything United Nations consider a threat
(TL;DR they are the resident anti-heroes, in a spoileriffic note, some of the main characters are their member)
FNC, aka Fallen Nation Corp, is a separate body on it's own. More or less similar to PT in canon, and larger than Fanon PT. They ARE the true villain Org.
@ Jak
I knew how you feel, moving is a bitch.