[En Sabah Nerd]

I'll chip in on the "where do Stormtroopers stand in the Imperial army?" conversation by pulling quotes from Star Wars' own website databank. The entry on Stormtroopers reads:
"Stormtroopers are elite shock troops fanatically loyal to the Empire and impossible to sway from the Imperial cause. They wear imposing white armor, which offers a wide range of survival equipment and temperature controls to allow the soldiers to survive in almost any environment. Stormtroopers wield blaster rifles and pistols with great skill, and attack in hordes to overwhelm their enemies. Along with standard stormtroopers, the Empire has organized several specialized units, including snowtroopers and scout troopers."

Let's all take a moment now and laugh at that part where it says they wield blasters "with great skill" because we all know how bad some of these guys are at aiming.
So Stormtroopers are officially considered shock troops and not just basic infantry (though this does raise the question of what the basic infantry units are?) but they have gear which is rigged to be adaptable. So Snowtroopers as we all know them (thank you Kenner toys) are technically Stormtroopers but wearing thicker, warmer attire. To quote from the portion regarding the battle of Hoth: "Stormtroopers in cold-weather gear deployed from Imperial AT-AT Walkers and invaded Hoth’s Echo Base." So to take it from Star Wars' own website all variants are technically Stormtroopers.