Direct flights are almost never on the same aircraft. Done potentially to save flight numbers, also to have "direct" service between two cities that don't have a nonstop and show higher on the list in GDS or OTA sites, etc. While I've seen it be same aircraft before, way rarer than to have a change. By the way, this is pretty much limited to the US - almost anywhere else in the world, a direct flight means a stop but scheduled with same aircraft. I.e. ACs YYZ-YVR-SYD - always same-plane service (barring IRROPS, of course).

For example, say OMA-ORD-LGA on one flight number. When doing a search, all else being equal, this flight will show above, say, AA (or even a different UA connection)with the same routing but different flight numbers. Even though in reality, it's no different. The connecting segment can even take off on time if the first segment is late and anyone on it would misconnect if booked through.

Direct flights don't always even have the same aircraft type. I know I've seen, for example, SMF-ORD-YYZ, one flight number, but where SMF-ORD was a 757 while the onward to YYZ is on a 319/320.