There are Tread pattern differences, which allows part of the tire to make good contact with the ground for performance (grip). Part of the tire with wide channels to evacuate water (typically called ribs), and sipes so the tire wears properly, etc.
An Asymmetrical tire is often referred to in the tire world as an inside outside tire, where a directional tires typically have a V pattern with the v point toward the hood of the car, and the 2 ends facing the rear. To answer the question of rubber on the surface or thread of the tire being different, this is incorrect it remains the same across the thread, while the rubber used for the sidewall in some cases is different. This describes the different terms typically used. while if you search for Goodyear you can find a tire with Kevlar in it which is stronger side wall. The inner side of the tire leads me to believe you might have a worn suspension part in the front causing premature tire wear, or that the alignment of the vehicle is off, I would post more links however I do not have the rep it appears.