To say that Saints Row IV is a completely different game to Saints Row: The Third wouldn't be correct. It's very similar, but the storyline forces the experience to be very different from anything previously in the series. After a rundown of the storyline, things will become a lot clearer.
Soon after the events of SR3, Pierce, Shaundi and Boss of the Third Street Saints gang are called upon to eliminate a terrorist threat. Boss kills the terrorist leader, then climbs aboard a launched nuclear missile and disarms it midair before it destroys Washington. Obviously, this makes him somewhat of a hero.
Five years later, Boss is elected President of the US, with his buddies as cabinet members. Soon after, an alien invasion results in Boss and the whole cabinet being abducted.
Alien warlord Zinyak places each of them in a simulation of Steelport to confront their own fears. It's up to Boss to break out and rally the others to defeat the powerful alien force.
It's this setting that presents a new level of gameplay, as within these simulations nothing is as it seems, and you can alter perception and gain superpowers to leap tall buildings and run faster than any vehicle. Think Crackdown meets Prototype, and you get the idea.
