Two lines in the same plane are if they have no common points?

They can be but need not be.

They could be parallel lines which, between them define a plane. Or they could be non-parallel, non-intersecting lines. Imagine yourself in a cuboid room with your back to a wall. Consider the line (A) formed by the wall behind you and the wall to your right. Consider the line (B) formed by the floor and the wall opposite you. The lines A and B have no point in common butthey are not coplanar.