Or to further elaborate:
The Trueno had the code AE86. The Levin also came as a AE86 (A souped-up version) and a AE85 (A base-model with a less HP engine).
In the USA, it was abit different. The GT-S had the AE88 designation. The SR5 had AE86. Plus both trims came with flip-up headlights, when the Levin had fixed headlights.
The Europeans have done that sort of thing, too.
In Europe, a 1986 Jaguar XJ6 is the "XJ40", the boxy Jaguar. In the USA, the prior car, the Series III, continued on for two years past the 85 cutoff date and finally terminated in the 1987 model year. So for two years (86-87), depending on market, you could have a car that had the "XJ6" badge (XJ40) that was completely and totally different from what someone else with the same model year car with the same badge had (Series III).
BMW did the same thing - during 2005 and 2006, your 330i could be either the E46 *or* the E90 body type, depending on your body style - and they were sold side by side on the showroom floor! They were making E90s and E46s at the same time!
And let's not get into mid-year or country-staggered launches. That just adds to the complexity, suffice it to say.
So, people use the model codes to indicate precisely which car they have. Helps for troubleshooting purposes.
Now, Toyota's use of codes is a bit weird. Most makers use their codes to refer to the overall chassis - XJ40, X300, E46, W201, etc., etc. Toyota goes so far as to change the model code based on what engine or option configuration it is.