Two distinct lines that never meet are called Parallel Lines.
On the coordinate plane, these two distinct lines will have the same slope.
Two linear equations that describe the same line will indicate the same slope, but a line is not a pair of distinct lines so the equations do not indicate parallel lines.
Two lines that intersect at right angles are called Perpendicular Lines.
Here's a construction that helps visualize the slope rule for perpendicular lines on the coordinate plane: http://www.wyzant.com/resources/files/264519/perpendicular_lines_slope_relationship_proof