You have exactly that you want except the little middle part is not a cylinder but an ellipsoïd!
The other part is a cylinder!
There is yes the same distance between Big "section" & "Little" section (ellipse) around it's axe

Always of that because your sections are not PERPENDICULAR to the perimeter !!!
Offset sections (ellipse) Extrude Sweep and finally Loft the little extremities between them