In case of parallel beam of light, the rays do not intersect each other throughout the propagation. The rays are equidistant from each other.
In case of convergent beam of light, all the rays meet at a point or appear to meet at a point during the propagation.
In case of divergent beam of light, all the rays diverge from a point. These rays originate from a point or appear to be originating from a point during the propagation.