The locator appears and shows the radius of the curve at that point. When you release the mouse button, the measurement is attached to the curve.
A point (cross) indicates the center of curvature (that is, the center of a circle having the same radius as the curve at the position of the locator).
The locator appears. You can move the new measurement while the mouse button is down. When you release the mouse button, the measurement is attached to the circle.