Let's take it from the top. For many pizza geeks, it doesn't get much better than a wood-fired oven built on site ("fixed," as in fixed in place) by one of the two remaining Naples families who still practice the craft, Ferrara (that's Stefano Ferrara pictured atop the oven at left) and Acunto.
Like a big-ass ol' house of stone*, these ovens are built on premises, and once they're in, they're in. If the pizzeria closes, God forbid, or moves, that oven stays — or gets ripped out by the next tenant (a tragedy).
* That's Chatsworth House at top if you're wondering.
OK. So this is where a lot of confusion can occur. Most people would walk into a pizzeria, see an oven like this beauty, and never, ever think of it as "mobile." It's hand-built as a unit off-site. It's then shipped whole to the pizzeria and placed on an oven stand, a journey that could presumably be repeated if the pizzeria changes location.
Think of it as the sleek prefab home above, which itself is built off-site then trucked in and placed on a solid foundation. Owners of both structures hope they'll never have to move them again, but they could do so if need be.
OK, so this is what I think most casual pizza-eaters think of as a "mobile oven." And up to a few months ago, it's what I thought of as "mobile," too. It certainly is mobile in the most obvious of ways. These trailer-mounted ovens are wood-fired and can often be found at outdoor festivals and at farmers' markets. In a trend I heartily approve of, pizza vendors who show up farmers' markets often top their pizzas with produce from neighboring stands.
Think of them as the stylish Airstream trailers of the pizza oven world. Wherever they park, they always get a good number of admirers, most of whom dream of buying one of their own, towing it from place to place.
Deck ovens consist of one or more baking chambers, each with a floor (the "deck") on which the pizzas are baked. Floors may be lined with brick (hence the "brick oven" in many a "brick oven" pizzeria name) or may simply be an aluminized steel surface.
These, to me, are the American Craftsman bungalow of the pizza world, the sturdy old workhorses of many a mom-and-pop pizzeria. Older examples may have quirks that the owner just has to live with and work around.
These are the conveyor-belt ovens in use by the major chains. Place a built-up pizza on one end of the belt, and in 4 to 6 minutes, a cooked pizza comes out the other. If you look at the third entry of Merriam-Webster's definition of impinge, you'll see it means "encroach," which in turn sort of carries the sense of gradual movement (though in a nefarious sense).
These are the McMansions of pizza ovens, spreading banality across the face of pizzadom.
extreme homebrew ovens
In the quest to make really great Neapolitan-style pizza at home without spending thousands on a backyard wood-fired oven, you have folks, like the Pizza Hacker, who have gone to some amazing lengths.
Jeff Krupman's PizzaForge oven, made from a Weber grill with custom refractory concrete modules, is like a really kick-ass treehouse. You look at it and think, I want to do that, too. (Krupman is currently working on a way to sell PizzaForge kits, so you might be able to before too long.)