Here's the short version.
The Spitfire Mk.9 was introduced as a stop-gap because the Mk.8 development was encountering many delays. The first production Mk.9 used the fuselage of the Mk.5 mated with the newest Merlin engine, the Merlin 61. Other changes include the adoption of twin radiator/oil coolers assemblies under the wings. Prior models had a one of each, the radiator under the right wing, the oil cooler beneath the left. Also it was fitted with a 4 bladed propeller.
The Mk.9 was so successful that it became the most widely produced Spitfire. Equipment was continuously upgraded as the war went on. The AH Spit9 is the earliest model.
The Mk.8 featured many improvements over the older models. The most visible is the retractable tail wheel and the enlarged tail surfaces, especially the taller, pointy-tipped rudder. The Spit8 is the fastest of the Merlin powered spits in level flight.
The Mk.16 is very similar to performance to the Mk.8 and far superior to the early Mk.9s. In reality, they are identical to the last production models of the Mk.9, the LF model. The major differences were the use of Packard Company built Merlin 266 models in America, whereas the technically identical Rolls-Royce Merlin 66 went into Spitfire LF Mk.9s.
Also, the Mk.16 used as different radio than the LF Mk.9.
In AH, the major difference with the Mk.16 is the armament is boosted by the use of two .50cal machine guns and two 20mm cannon. The older models use four .303cal machine guns instead of the .50cals. Also the AH Mk.16 has the short "clipped" wing tips. These improve the roll rate and diving speed of the aircraft over the full length tips.
To summarize the AH spit lineup based on widespread availability in reality:
Spit1 - 1940 model
Spit5 - mid 1941 model
Spit9 - late 1942 model
Spit8 - late 1943 model
Spit16 - late 1944 model
Other:
Seafire Mk.2 - 1943
Spit14 - late 1944 high altitude model with Griffon engine.