I would say that they are sometimes on the same line. Think of the following scenario: a line, AC, is bisected by point B. You do indeed have two rays, each representing a part of the line.
Another scenario, think of a standard number line. Say AB goes from -1 to -3 and then continues to the left. BC goes from 2 to 4 and then continues to the right. These are two rays, each pointed in opposite directions, but on the same line.
