Two lines that intersect and form 90-degree angles (right angles) are "perpendicular" to each other. You would call them "perpendicular lines."
Two lines that are equidistant and, therefore, never intersect, would be parallel lines.
Two lines intersect at a point
They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.
Parallel lines do not intersect.
Two lines cross or intersect at a point.
Two lines that do not intersect on the same plane are Parallel lines.