Does a 1.25" eyepiece not use the objective as 2"?

Does a 1.25" eyepiece not use as much of the objective lens as a 2"
eyepiece?

All tubes have a focal length at which there is a focused image. If a
smaller eyepiece captures less of this focal plane than a larger
eyepiece then there is loss.

I'm no lens expert but it seems that a larger eyepiece would capture
more of the focal plane. A smaller eyepiece wastes some of the focal
plane.

Is this true or does a smaller eyepiece use as much of the objective
lens as a larger eyepiece?

Thanks for your help.