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If they are in the same plane, then they share a common plane. Did you mean to say common point. If that's the case where they are in the same plane, but do not share a common point, then they are parallel lines.
Co-planar means being in the same plane.
If you mean the plural of plane, it is planes. If you mean the spelling of another word that is pronounced the same way, it is plain.
coplanar lines just mean that two lines are on the same plane. If they do not intersect, that means that they are on the same plane and are parallel to one another
Coplanar means on the same plane. As co-linear means on the same line.