It's explicitly clear in TO-01-75F-1 that the maneuver position of the flap control lever will deploy the flaps 1/2 way. In variants before there was a maneuver position, the pilot had to pull the lever to "OPEN", watch the flap indicator, and then push it to "CLOSED" when the gauge said it was at 1/2. The addition of a maneuver position was merely a change in the hydraulics, to lessen the work load on the pilot. This Tech Order manual covers F-4 through G variants, so it gives notes for both situations.
As far as the degrees of deflection, I have always taken what may be interpreted as a discrepancy to mean that the specific mechanics of the fowler flaps hydraulic throw range isn't linear with the degree of flap deflection. You can see this in the diagram AKAK posted. If you reference only the horizontal travel of the flap hinge point, the position marked "maneuver", is 1/2 way horizontally between "retracted" and "landing".