I use a flight simulator (X-Plane) to practice instrument approaches and have used FlyThisSim at the local flight school for training. However, these are not flight simulators in the eyes of the FAA so you need to understand the terminology in order to log the time on them.
A good place to start is AC 61-136A Aviation Training Devices. This lays out the difference between Basic and Advanced Aviation Training Devices. The FlyThisSim device meets the qualifications of a BATD. You can find their Letter of Authorization (LOA) on their website. Even though I am running the same software on my computer, it doesn’t meet the requirements for an Aviation Training Device so none of the time is loggable. The Redbird systems more sophisticated and are Advanced Aviation Training Devices.
You can use the time in an Aviation Training Device to fulfill part of the experience requirements for various pilot ratings. The part that was confusing to me was the ability to maintain currency for IFR flight. Here’s where the difference in semantics becomes important. A BATD or AATD is not a flight simulator or flight training device. Therefore you can use it to maintain IFR currency if you comply with §61.57 (c) Instrument experience. but only the third section.
(3) Use of an aviation training device for maintaining instrument experience. Within the 2 calendar months preceding the month of the flight, that person performed and logged at least the following tasks, iterations, and time in an aviation training device and has performed the following—
(i) Three hours of instrument experience.
(ii) Holding procedures and tasks.
(iii) Six instrument approaches.
(iv) Two unusual attitude recoveries while in a descending, Vne airspeed condition and two unusual attitude recoveries while in an ascending, stall speed condition.
(v) Interception and tracking courses through the use of navigational electronic systems.
§61.51 Pilot logbooks. details the requirements for logging time and requires an instructor to be present and sign the logbook if an Aviation Training Device is used to satisfy the recency requirement.
(g) Logging instrument time. (1) A person may log instrument time only for that flight time when the person operates the aircraft solely by reference to instruments under actual or simulated instrument flight conditions.
(4) A person can use time in a flight simulator, flight training device, or aviation training device for acquiring instrument aeronautical experience for a pilot certificate, rating, or instrument recency experience, provided an authorized instructor is present to observe that time and signs the person’s logbook or training record to verify the time and the content of the training session.