There are actually 2 answers to this question. First, if they are in the same plane they are parallel. Second, if they are in different planes they are skew.
The point of intersection.
point
A point.
If the lines are identical, then the whole lines. If not they can either not meet at all or at a single point: the point of intersection.
Intersection.
intersection
point
a point
It is usually called an intersection or an intersection point.
The point where two or more lines meet is the intersection.
point of intersection
I think you're talking about an intersection. An intersection is where two or more separate lines meet each other in one point.