Does stalling an engine count as lugging it? I know lugging is not good for the engine for various reasons. Does stalling do those to the engine as well? Thanks
Think of stalling an engine as lugging it once. While not good for your engine/car, it won't do the same damage which is possible with lugging your engine. Stalling the engine is basically the engine not having the torque to overcome the demand which has been put on it.
As far as lugging damage, check this answer. Lugging an engine can cause real damage.
Running at low revs "lugging" is not really damaging provided you have appropriate oil pressure, but I'd question the mileage gained by it, modern ECU's will provide appropriate fuel and may run richer trying to raise these speed when you're trying to accelerate from an already high gear. Modern engines are far more tolerant than engines of decades past and are not likely to suffer any internal damage.
The only real concern I would have would be additional wear and tear on items such as engine mounts, transmission mounts and your clutch if you're driving a manual car if you are unable to keep the car from bucking at such a low rev.
Stalling isn't really as bad as people would have you believe IMO, more of an inconvenience or embarrassment. Teaching many people to drive manual transmissions over the years I've never had a stall induced breakdown.