Those are good questions about measuring the efficiency of the fuel vs that of the appliance, and I don't know the answers, precisely. From my experience heating with wood, I can tell you that the efficiency of a stove refers to its ability to extract the maximum amount of heat from the fuel. It's measured in various ways. But basically, a cord of dry locust will contain x BTU's. Stove A will burn it and produce a percentage of that, while stove B will produce a different percentage.
Much has to do with the amount of the fuel that actually gets burned. Combustion requires fuel, air and heat. Much flamable gas leaves the burn zone without combusting because it never encounters air and heat in sufficient amounts before it gets sucked out of the stove. A more efficient stove puts the right amount of air, heated to the right temperature, in the right place. Likewise, a flue that is too cold won't draw enough air into the burn zone; one that is too hot is burning some of the fuel after it's left the combustion chamber and it goes up the chimney. All stoves aren't equal and internal design matters, but an inefficient stove gets more heat out of a unit of fuel than an open flame does, just by managing the above three requirements better. And by absorbing some of the excess heat to radiate after the fuel burns out.
I don't know how manufacturers tweak their numbers to their advantage, but I'm sure they do and personally I don't take them seriously. Outside temp, flue temp, room air temp, humidity and other factors affect whether my stove burns as efficiently in my boat as it did in the lab that tested it. I wouldn't expect every Newport 9000 to produce 9000 btu's uniformly. I'd just expect it to produce less than a Newport 12000. About the only thing we can predict or control is how well we insulate.
Probably more than you wanted to hear, but it's about all I have to think about during the long northern winter.