skew lines
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Parallel lines would always lie in the same plane. They would need to be skew lines.
They're either parallel lines or skew lines.
There is no specific term but you could try "non-coplanar".
Two lines that lie on different planes but are not parallel.
Skew lines are lines that lie on separate planes. and do not intercept parallel lines that are sometimes on the same plane, but don't intersect