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AE## is the chassis code for the Corollas,

AE86 = 85-87 RWD Corollas both GTS and SR5 (AE82 was the FWD model from 85-87, which was available in 4 door and 2 door hatch which was also known as the FX16 which also came in GTS and SR5)

AE92 = 88-92 FWD Corollas. available in GTS and SR5 in 2-door models, and base and LE in 4-door models.

SR5 = No balls or whistles base model , came with an 80hp 4AC (carburated) motor from 85-87, a 90hp 4AF (carburated) motor from 88-89 and a 100hp 4AFE (fuel injected) motor was also available from 88-92.

GTS = More balls and whistles, comes with a 120hp 4AGE from 85-89 and a 140hp 4AGE motor in 1990.

GTZ = All balls and whistles, not available in north america, came with a 140hp supercharged 4AGZE motor from 88-89 and a 170hp supercharged 4AGZE motor 90-91.

I Know the AE92 also came in wagon models, not sure about the AE86 though. The AE92 wagon came in FWD and AWD models and I believe they had the 4AF and 4AFE motors, but I could be wrong.

here's a good link for ya.

http://www.toyotanation.com/forum/t18776.html

Some more facts, In Japan AE## cars came in different models

-Corolla (4door) and Corolla Levin(2door)
-Sprinter (4door) and Sprinter Trueno(2door)

here's an AE92 Trueno



AE92 Levin



AE92 FX16 GTS model



AE92 4 door model



AE82 FX16 GTS model



AE82 4 door model



AE86 Levin



AE86 Trueno