How to select edge rings between two edges? Holding Ctrl you can select the Shortest Path between two selected egdes.
This essentially allows you to select a range edgeloop.
Like so: 



Ctrl+Alt+LMB will allow you to select and edge ring like so:



But how do I select the shortest path edge ring? Or rather, a range of edge rings between two selected edges.
It may be easier to use another selection tool instead of Edge Ring selection, because it won't take into account specified end of selection.

You can workaround that by selecting faces:


Select the shortest path with Path Selection in Face Select mode.   
Switch to Edge Select mode, and deselect top and bottom edge loops by holding Alt+Shift and clicking with LMB on them. "Shortened" edge ring will be the only left selected.