A 4-way stopcock allows for 360 degrees of rotation and has the states (shown below) for each of the four available positions. A 3-way stopcock has only three positions and has the first three states shown below.

In the first state, liquid flows between points A and B.
In the second, it flows between points A and C.
In the third, it flows between points B and C.
In the fourth state (4-way only), it flows between all three points.