Two points are always colinear, but a third point is not necessarily on a line joining or passing through the other two points. Imagine the two points forming part of the edge of a plane. Using the line joining them as a hinge the plane can be moved so as to uniquely include the third point, so the points are then coplanar. One plane includes all three points, and it is the only plane to do so.
Going back to each of the two points, call them A and B, the third point C can be joined by a line so A and C can be on a separate plane from the plane that contains A and B. Similarly, a second plane can contain B and C. So we have four configurations: one plane containing all three points and three different planes each containing a pair of points: AB and AC, AB and BC, and AC and BC. So the three non-colinear points (not all three are in line, but two out of three must be) don't all lie on the same two planes: a pair of points only lies on each of the two planes, the third point shares a plane with only one of the other points.
Does that seem clearer?