The 3 games take place in the same World, Ar Ciel, but different parts of it. The three towers that are the only inhabitable place that remained. The inhabitants of each Tower usually refers to their Tower as "world" because they don't know that there are other Towers in the dead world that is Ar Ciel.
And each Tower has a Origin yes so you get three Origins. Shurelia and Tilia know each other but Frelia doesn't know and isn't known by the two. Shurelia did meet Frelia in At2 Binary Field though. Shurelia and Tilia met when Tilia was born at the first Tower (Shurelia's Tower) and before she was sent to Sol Cluster where she would have her own Tower.
People are paid to do Lolita Sonwellia's dirty work.~♥
Thanks iruje for the sprite and Geiky for making it into an avie.