Simulator time counts toward "Total Pilot Time" but not toward "Total Flight Time".
"Total Time" isn't really defined in the FAR. When the term is used, it's not alone. For example, the 61.159 aeronautical experience requirements for the ATP include "at least 1,500 hours of total time as a pilot" So there's really no such thing as "TT" standing by itself.
It's usually combined with either "pilot time" or "flight time". And there is a definite difference between these two terms.
"Pilot time" is defined in 61.1(b)(12) specifically includes simulator time.
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that time in which a person -
(i) Serves as a required pilot flight crewmember;
(ii) Receives training from an authorized instructor in an aircraft, flight simulator, or flight training device; or
(iii) Gives training as an authorized instructor in an aircraft, flight simulator, or flight training device.
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On the other hand, "flight time" is defined in FAR 1 as
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Pilot time that commences when an aircraft moves under its own power for the purpose of flight and ends when the aircraft comes to rest after landing; or
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That doesn't include simulators. Even the best of them are still not "aircraft"
The logbooks I've seen don't have a column for "total time" or "total pilot time". They do have a column for total "flight" time or "Total duration of flight" and sim or FTD time doesn't belong there. Want to track total pilot time? Add a column and go ahead. It counts for something.