What is the precise definition of "routing"?

Is it
(a) just the cites that you go through
(b) the cities that you go through and the order of them (in the case of a trip involving a change in two or more locations)
(c) either a or b above as well as the carrier
(d) if the carrier matters, is it only the marketing carrier, or also the operating carrier? Specifically, what about commuter arms of major carriers?

Also, if the routing is as you specified in the first post wiht AA on the outbound and UA on the return, but the UA portion of the tarriff allowed for a stopover in ORD, and that had been exercised, would the presence of the stopover have have altered the routing?