What are the differences between "Off/On Time", "Total AC Time", and "Offset"?
There are different definitions for times in the U.S. FARs.
For example FAR §1.1 has a definition for flight time

Flight time means:

(1) 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
(2) For a glider without self-launch capability, pilot time that commences when the glider is towed for the purpose of flight and ends when the glider comes to rest after landing.


This would typically be your OUT and IN time.
The Hobbs meter (depending on how it is wired) indicates the hours the engine is running or the hours the airplane is flying.
FAR §1.1

Time in service, with respect to maintenance time records, means the time from the moment an aircraft leaves the surface of the earth until it touches it at the next point of landing.

FAR §91.409(b)

Except as provided in paragraph (c) of this section, no person may operate an aircraft carrying any person (other than a crewmember) for hire, and no person may give flight instruction for hire in an aircraft which that person provides, unless within the preceding 100 hours of time in service the aircraft has received an annual or 100-hour inspection and been approved for return to service in accordance with part 43 of this chapter...

So the OFF-ON times are used for maintenance intervals.
I am personally unaware of total aircraft time or offset.
Most FMS installations have the ability to capture this data automatically.  It is called the OOOI value or OUT-OFF-ON-IN times.  Use the OFF-ON for maintenance and the OUT-IN for pilot logbooks.