PS3 was one colony ship. PS4 didn't involve any colony ships. Only mentions were made of them such as the crashed one to the east of the guilds town.
I don't remember exactly what it was, but I remember there was a strong plot link implying the world of PS4 happened 1000+ years after PS3. Which is why I included them together in my mini-summary.
Edit: I remember, one of the androids in PS4 was in PS3 and mentions some of the PS3 plot elements.
At least we can take solace all the PSO/PSU assholes are already dead before PS4.