A lot of this depends on what you mean by "the same model" - there is a lot more variation between aircraft than there is between cars, and a lot more that the pilot can customize. While every Ford Mustang you get in will be relatively similar even if you're going from mid-1960s to early 2000s models you could get in two planes that came off the assembly line right after each other yet seem completely different depending on what their owners have done to the avionics and airframe over the years.
On top of the avionics and panel layout and possible engine performance variation every aircraft is different: for the most part they're hand-assembled (even airliners to some extent) so there's variation there, and planes last a long time so each one has aged differently.
One airframe may have been in accidents and had major repairs that weren't quite to spec, another may have rigging issues (I flew a trainer that required left rudder in a right turn to remain coordinated), so you have to develop a feel for each plane you fly.
As another example of variation between planes consider that both Cessna and Piper have produced very long-lived "models": Cessna's 172 and Piper's Cherokee family (which I've picked because both are still in production today).
By one measure these are the same "model" (It's a Cessna 172, or a Piper PA28), and they'll fly largely the same as any other plane of the same type.
By another measure there are many different models in each family.
For example you could have a Cessna 172 E with mechanical flaps, or a Cessna 172 F with electric flaps. You could have a Cherokee C model with "barn door" air vents and overhead trim, or an E model with the vents in the wing root and a trim wheel between the seats.
Sometimes these differences won't matter much to the pilot - the difference in air vent location in the Cherokees doesn't really affect your flying. Other times it's a difference you need to be aware of, like whether your flap controls are a switch on the panel or a lever on the floor in the Cessna, or whether you reach up or down for trim in the Cherokee.