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I was reading about Atlas B763 that was involved in an accident on Feb 23rd, 2019. Based on what I read plane was 25 years or so old.

As a person who has no relationship about aviation industry except occasional flying as a passenger, I'm curious to find out if these planes also have generations or models like car manufacturers do e.g. Honda civic, 2015, 2016 or 2017 models where there are small but distinct changes.

Based on Wikipedia pictures, cockpit photos are different for various generations as technology is improving/changing.

Are pilots rated on particular generation of the plane or once you are rated on B763, you can fly any one of them whether it was built 25 years back or yesterday?

While airliners don't have "model years" like cars do, they are certainly changed over time.

There are major "generations" of some aircraft types, like the 737. The "original" (-100,-200) was replaced by the "Classic" (-300,-400,-500) which was replaced by the "Next Generation" (-600,-700,-800,-900) and most recently replaced by the "MAX" (-7,-8,-9,-10). While technically still the same aircraft type, there can be major differences between them, especially from the pilot's perspective.

The 767 hasn't had any major "generations," but it has had multiple models, as is common with airliners. These are mostly just adjustments to fuselage length, fuel tanks, and structures. Other than small changes to systems, or different guidance to prevent a longer fuselage from stiking the ground on takeoff or landing, there is minimal training required. The 767 cockpit was even designed to be common with the 757 to minimize required training.

The FAA requires pilots to get a specific "type rating" to fly any aircraft over 12,500 lb max takeoff weight. The scope of this rating is negotiated between the manufacturer and regulator like the FAA. This could change with new versions, as with the 747-400, or even be common, as with the 757 and 767. There may also be training for each minor model, though not as in-depth as a new type certificate.

There are also changes made within the minor models over time. The biggest changes would probably be things such as modifying the winglets or adjusting the engine installation to get better performance, or a new cabin interior design. There are also many smaller changes that occur throughout the airplane. There isn't really a regular schedule for these like in the car industry, as there's less turnover in the aircraft market and major changes can be very expensive to certify. There would have to be a significant benefit to make a change requiring new pilot training, which is why those changes tend to happen in the more major "generations."

Pilots will have a "Type Certification" that ensures they have been trained and can operate a specific model, or group of models that have identical cockpits. The classic example is the 757/767, the 757 being a narrow-body and smaller plane, but both have the same cockpit layout, so a pilot can go from one to another without issue.

This FAA Document (PDF) lists the type ratings for each aircraft. You can see that the 757 and 767 share a type, as do the A318/319/320/321.