The FAA certification of Full Flight Simulators FFS ranges from Level A through D. Although Levels A and B simulators exist, in practice new ones are generally not built and certified. Levels C and D are the standard full motion simulators you see used by most airlines. Like the FAA standards for Flight Training Devices (FTD) they are dfined in 14 CFR 60. Like the FTD specification it would be impossible to distil the content here down to a readable summary as it is hundreds of thousands of words. If you're not an AFS-200 airline an FFS is probably of no interest to you.
A Level C or D FFS must accurately replicate every aircraft system available from the cockpit and that replication is measured in an objective way.