Modal analysis computes the frequency shape of modes and displays a magnitude of displacement that has no meaning for the displacement of a real structure because there is no load applied to the structure in a modal analysis.

To obtain displacement magnitudes of real structures, you have to apply a load and see the response.  You can only apply a load in a Transient Structural or a Harmonic Response analysis where zero load = zero response, in other words, you have to apply a load.  In Modal Analysis, you are not permitted to apply a load.

When you have a rotationally symmetric structure, ANSYS will report two modes at the same frequency, one mode bending around the Y axis and another mode bending in the same way around the Z axis (assuming the axis of rotation is the X axis).  Mathematically, they are the same mode, just with different orientations. You are getting that effect but the frequencies are not quite equal. If you refine the mesh, they may get closer together.