Non-coplanar lines. They could be parallel or skew.
For example, consider yourself facing a wall in a cuboid room. Line 1 = where the floor meets the wall in front of you, Line 2 = where the ceiling meets the wall in front of you, Line 3 = where the floor meets the wall behind you. Then Lines 1, 2 and 3 are parallel but not in the same plane.
Or
Line 4 = where the walls to the left and behind you meet. Lines 1 and 4 are not parallel nor in the same plane: they are skew.
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They are called skew lines.
They are parallel lines
2 Lines in the same plane that do not meet are parallel. If 2 lines are in different planes and do not meet, then they are called skew lines.
Non co-planar lines are lines that do not lie in the same plane.
If they are not parallel and do not intersect then they would not be in the same plane (not possible), but they would be called skew lines.