It's recommend you read the page on Entry Level Flight Simulators before this one.
As with the article on entry level sims we're talking about a conceptual idea here, not a regulatory classification. These would typically include FAA approved Advanced Aviation Training Devices (AATD) and FAA approved Level 5, 6 and 7 Flight Training Devices (FTD). These devices generally do not move, but some do1, usually only in 3 degrees of freedom2. At the top end they may include realistic vibration systems3. We're going to leave full motion simulators (Full Flight Simulators) into their own category.
These simulators generally emulate a category and class of aircraft, but some are built to be a specific aircraft. Often you will see these kinds of simulators advertised as simulating a list of aircraft within a class, and that makes them versatile tools, but also affords less transfer of skills from the simulator to a specific aircraft. Some will specify that they represent only one aircraft. These usually have very high fidelity to that particular aircraft and can be amazing training tools for familiarizing users with a specific aircraft.
What we would consider high fidelity, or complex flight simulators generally very closely match a real aircraft both in terms of the appearance and layout of the physical cockpit, and usually in terms of the virtual aircraft's flight performance. They will also generally have excellent visual systems; having both large immersive displays, and pleasing graphics with rich textures. All of this effort in producing a more realistic simulator (high fidelity) which can replicate most or all of the systems (complex) in an aircraft serve to produce a more immersive training environment. A higher degree fidelity leads to greater immersion (often called presence in virtual reality contexts) which leads to a smoother transfer of knowledge skills learned in the simulator to the real world. The greater replication of aircraft systems allows for more versatile and nuanced training scenarios.
These simulators generally have complete physical controls, unless the aircraft being simulated has a touch screen all the switches will be real switches, and generally most will work just as they do in the real aircraft. Perhaps not every breaker will be simulated, and not every warning light will be present but they're to a much higher level than the entry level simulators, and indeed many do simulate every system. They don't have to be complete replications of a specific aircraft though, and not every situation must be able to be simulated. This is a case where the simulators may go beyond the requirements for the regulatory classifications they are certified to. For example an FAA approved AATD is not required to simulate icing conditions, though it is recommended, and most will.
The difference between FAA approved Aviation Training Devices (BATD / AATD) and FAA approved Flight Training Devices (FTD)
Aviation Training Devices or ATD for short (available as a BATD or AATD) are products produced by a manufacturer who has them tested and approved by the FAA. You can purchase one and it is already approved within the bounds set out in its Letter of Approval (LOA). BATDs and AATDs come under the cognizance of AFS-800 the General Aviation and Commercial Division of the FAA. That approval may be conducted at the manufacturer or a specific flight school where the device resides. It is global in nature in that the requesting party is generally the manufacturer. The LOA usually has a term of 5 years after which time it must be re-approved. A Flight Training Device (FTD Level 4-74) is approved by the FAA’s AFS-205, National Program Simulator Program Office. AFS-205 is under the 200 branch (Air Transportation Division) which is cognizant on all airline and on-demand charter operation. Simulators at this level are generally built for a specific use by a specific user, in a specific way, for a specific time. It's a "site approved" device, meaning you contract one to be built and it receives FAA approval after it is installed and that approval is conditional and must be renewed every year. The approval is the responsibility of the user and not the manufacturer, although the manufacture does assist the user in getting approval. The FTD is more work and more expensive but can be approved for more time and tasks than the lower level simulators. That said, most Level 5 FTDs and AATDs are useable for the same number of hours towards FAA certifications. However FTDs tend to be built to a higher fidelity and include a more complex simulation of systems. The main difference and cost driver is the approval process. For FTDs that process is more complex with much more objective rather than subjective testing required.
Motion doesn't automatically mean a better simulator, it's a somewhat controversial topic we cover more deeply on our page about flight simulator motion. At this time of writing the FAA is encouraging AATD manufacturers to include motion (AC 61.136 Appx. 3 § 3 ss. b p. 2) ↩
The 3 Degrees of Freedom is a reference to being able to rotate along the Pitch, Roll, and Yaw axis, not a measurement of how far they move. ↩
An accurate vibration system is a requisite for a Level 7 FTD ↩
In practice although Level 4 FTDs can still be certified, they are generally not produced as they are generally Parts Task Trainers which for most users generally don't benefit from having an approval. ↩