How to get uniform mesh between 2 extruded volumes (2 concentric circles) when the inside volume is rotating and outer volume is linear

Question

So, I have been working on a gmsh 3.0.2 geometry, which requires me to create 2 concentric circles, and then extrude them, after extrusion, I have:

1. Inner cylinder (with grooves)
2. Outer annular ring

When I mesh, I want the mesh nodes to be consistent on the interface. either they should share the same mesh nodes at the interface or any other feasible alternative.

P.S.: I don't want to rotationally extrude the outer cylinder also, can a Boolean operation be used in such cases?

The inner volume is a helical extrusion and the outer volume is linear.