You're both wrong. AE85 and AE86 refer to the chassis, not the engine. the AE85, however does have a different engine, but that's only one of the differences.
The USDM Corolla SR-5 is an AE86. It has exactly the same chassis as the GT-S. However, it has an SOHC, carburated, 4AC engine instead of the DOHC, fuel injected, 4AG, lacks a Limited Slip Differential, and has a differently tuned suspension setup, and several asthetic changes, different paint schemes, a different bodykit, and a slightly different interion.