Both Audi Quattro and the 4th gen center diff use a planetary Torsen T3 (also known as type C) which is biased towards the rear. They're literally the same mechanical system. So, like you said, semantics. AWD and Full-Time 4WD are marketing terms. One sounds tough and truck-like, the other sounds cool slick.
That doesn't change the fact that Audi's set-up is a single stage and less robust system; in most cases it's just a tiny ring gear and pinion bolted on to a transaxle/transmission. Versus the 4Runner's dual-stage, chain-driven transfer case. Yes they both use a Torsen T3 for the same desired function (to power both axles without the front axle binding in turns), I will concede that a "Ful-Time 4WD" system with a Torsen T3 like the 4Runner's is probably as close to a "hybrid" AWD/4WD system as one can get as you get the on-road flexibility a AWD system provides with the robust durability of a true 4WD system; but it doesn't change the fact that they are essentially two separate systems.
Most every 4WD system I have seen in a 4WD vehicle is a multi-stage system designed towards a near 50/50 split when engaged, with an often chain driven transfer case that has one or more gear reductions (older systems were gear driven so I won't rule them out completely).
The biggest distinction I would say is that AWD systems are designed mainly for Cars and CUVs and are typically biased with no gear reductions sets. They also have very few actuated parts (some do have a "Center Differential Lock" feature to try and make up for their inherent bias, but even this is often electro-magnetically controlled with a magnetic clutch pack, such as in the Rav4 and Highlander. Where as CDL in a 4WD system is mechanically engaged by physically locking gears such as in the 4th gens). 4WD systems on the other hand have typically have one or more gear reductions, provide near 50/50 torque split when engaged, and are more robust at handling that torque. Which is why you see them in Trucks/SUVs mainly.
I have not seen a car with a dual stage transfercase or anything other than an "add-on" differential like most FWD biased AWD systems used. Conversely I have not seen a true Truck or SUV with a single stage "add-on" AWD system. There are some CUVs that use a dual-stage system, but those are all advertised as 4WD not AWD and while I consider them vile uni-trash imposters; they are for the most part running a Truck/SUV system not a car AWD unit.
Functionally they do both power all 4 wheels, but as I said before the distinction is somewhat semantic at first glance, but becomes important when you realize that they are designed and function differently. They also drive, operate, and perform differently as well. It'd be akin to saying that an independent rear suspension and solid rear axle are the same thing because they both drive the rear wheels and they both can have LSD/lockers in them. But while similar in function and components, they are designed and operated much differently.