I have 2 cylinders where I make a difference with boolean modifier. After applying, I see in the Edit mode that there are 2 edges connecting the outsite with the inside. Is there a way to avoid this or to join the separate faces?
If you want to convert that Ngon into quads delete it and use Ctrl+E > Bridge Edge Loops; it should work nicely if amount of vertices is the same.
However you can use more convenient way in order to construct cylinder like on your screenshot.