As someone who works on commercial flight simulators I hope I can help answer your questions.
In a typical training environment you find the following:
Computer Based Training
Custom designed applications are provided by various manufacturers and they are designed to represent/simulator the entire aircraft, or they can focus on a specific system like the Flight Management System.
These tools are valuable because they can run on most any computers, and even tablets now, thus allowing the student to learn at their own pace without tying up an actual training device.
Flight Training Devices
These are physical mock ups of the aircraft cockpit in question, there are various levels that these can be certified to that (mostly) relate to the hardware configuration. These are typically used for initial training only. These are fixed based and usually do not include any out the window visuals.
Full Flight Simulators
A full flight simulator provides a complete representation of the simulated aircraft in question. It consists of a fully accurate flight deck, a visual system, a control loading system and a motion system. There are 4 levels of certification a full flight simulator can receive (A, B, C and D) with D being the highest one currently. A level D simulator consists of a 6 degrees of freedom motion system as well as a wrap around collimated visuals. Level D simulators must provide additional special effects and cues to the pilot and there are more quality tests that are required to be run to demonstrate the simulator matches the aircraft.
To answer your question, airlines most definitely do make use of full flight simulators and they are incredibly useful. The average level D simulator might cost $15 million dollars but it is a small fraction of the cost required to train on the real aircraft (factoring in fuel and maintenance etc.), stats I've read show that FFS training can be as much as 1/40th the cost of using the real aircraft. In addition to the cost savings, they allow crews to train for situations that would be too dangerous or impossible to simulate using a real aircraft (for example a sudden engine seizure at V1, among many others).
The advantage of a level D simulator is that it is certified to allow zero flight time training, where the first flight a pilot flies is a revenue flight. Full flight simulators are used in both initial and recurrent pilot training.