I think monetary policy is the primary axis upon which these two schools are separated. Chicago is under sway Keynes when it comets minatory policy-- but note this is not the same as keynsianism which is a modern political theory that ignores the repercussions of easement that Keynes warned about.

Austrians are pretty much hard money. There are some interesting comments made by rothbards and Friedman about each other ot illustrate the split.

The schools reach similar conclusions on a number of issues, though.

You already accepted they are separate, I'm just trying to add flavor here, not win a point.