Ae86 has nopthing to do with the year 1986.
in toyota speak
A=powered by "A" family engine - the 4A-g
e=corolla
8=8th generation
the digit after the 8 is the model. Ae82 is a front wheel drive four door and the ae85 is an economy model ae86.
to the best of my knowledge the history of sporty Ae cars is something like this : Ae71 Ae82 Ae85 Ae86 Ae92 Ae101 Ae111 . Before the 4a-g Sporty corollas were powered by the T family engines like the 2T-g so the sporty corollas are called Te21 and Te27.