AWD: All wheel drive is always on. The power fromt he engine goes to basicly a differential that will split the power from the front axle to the rear axle while still providing "slip" so that the front and rear tires can turn at different rates, and still be driveable. AWD vehicles aer usually light duty, and do not have to deal with the torque transfer of a 4 wheel drive. AWD power systems usually put 100% of the torque to the rear tires until tire slipping is sensed, then power begins to be transfered to the front. ( some, such as subaru work the exact opposite way, power goes tot he front, then when slipping is sensed, it transferes to the rear ) AWD only have one transfer case speed, high. Meaning the transfer case can not reduce the gearing, it just transferes the torque.
4WD: 4 wheel drive is switchable. If a vehicle is true 4 wheel drive, the ability to go to 2 wheel drive ( rear only ) exists, and is made to be operated that way. Torque goes from the engine, then is split 50-50 from front to rear. No sensing exists, it always splits torque 50-50. The splitting is done by a very large chain ( usually ) and the chain has no "give" in it for slippage. Without that slippage, you can get some wierd handling around cornders and at high speeds because the only way for the tires to spin at different rates is for one to "scrub" on the pavement. That is what causes most tire wear. also, in most 4wd vehics if you make a sharp turn, you will tend to "plow" or keep going straight. 4WD vehics also have a "low" range, where the transfer case reduces the gearing, to get more torque, but slows down top speed. (in low, I am at redline in 4th at about 40 mph ) but the power increase is huge. Also, 4WD is manual selection. The driver must manualy pull a lever to put the vehic in 4WD or low, while a AWD the car does it for you. 4WD parts are also 4-5x as big as AWD, as AWD is just meant to move the car, 4WD is meant for desert womping, mud running, or pulling AWD cars out of ditches.
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And yes, 4WD and AWD cars use more gas than the same vehic with 2WD, as parasitic losses are incurred by the transfer case, and the other axle parts.
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