Unfortunately they go deeper that that. Type also takes into account handling characteristics. RAAus Ops have stated that if you learnt on a J160 you would need a type endorsement to fly say a Savannah. Common sense to get checked out on different aircraft but they have removed the ability of experienced pilots (say CFIs) to self endorse. Definition of type from ops manual is below. In my opinion this will come back to bite if an incident occurs and a pilot has not been formally type endorsed as per the ops manual. Don't take my word for it, ask Ops.
Aeroplane Type
Aeroplane undercarriage configuration, design features, flight envelope (e.g. high drag/low drag and considerations of inertia), stall speeds and normal/emergency handling characteristics as designated by the manufacturer.