Difference between "intercept" and "intersect"

Solution 1:

There is a temporal element to intercept which is absent from intersect: if two paths are generated respectively by two particles moving through space, the paths may intersect; however, one particle only intercepts the other if they arrive at the point of intersection simultaneously.

Solution 2:

The words "intercept" and "intersect" sound very similar but mean different things.

"Intersect" is a binary (two-valued) qualitative property of two or more sets and means that they have points in common, e.g., curves cross or areas overlap etc. Those points in common are called their "intersection." So, for example, every pair of sides of a triangle "intersect" at a point called the vertex of the triangle. In fact the word "vertex" REFERS to the point where two sides of a triangle meet. So as The Chaz commented, "intersect" is a verb.

On the other hand, an "intercept" is a quantitative property of of a curve. It refers to a specific point where the curve INTERSECTS one of the axes of the coordinate system, the particular axis lending its name to identify the intercept, such as "x intercept," etc. So an "intercept" is a particular intersection, usually referring to that point of a curve that is in common (crosses or first touches) another curve, usually a coordinate system axis.

Solution 3:

An intersection point is a meeting point of two straight or curved transversal lines.

A length of line included between two points of intersection is a line segment or intercept.

A single line is a segment between its endpoints but is not an intercept.