A Hobbs meter that is started when you turn on the battery master is probably the least accurate method of determining Air Time or Flight Time.
The pilot in command is responsible to determine the correct air time and flight time for each flight they operate.
Aircraft rental companies, and individual aircraft owners, often make up there own procedures for recording air time and flight time that are not necessarily accurate or legal.
The FAA Air Regs make no mention of any sort of hour meter. The best source for recording air time or flight time is the clock in the aircraft or the watch on your wrist.
“HOBBS” time has no legal status. This is especially true since there is no standard on how an hour meter is activated. Some hour meters start when the battery master is turned on. Some start when they sense engine oil pressure. Some start when only when the aircraft is airborne.
“TACH” time also really has no legal standing as it is RARLEY accurate for flight time or air time.
The fact that Hobbs or Tach time are routinely used in pilot and aircraft log books is just an example of convenience and laziness.
“Off/On Time” represents the actual time on a clock at the moment takeoff and landing, and used to calculate the actual air time for a particular flight.
“Total aircraft time” represents the total accumulated Air Time or an aircraft.
“Offset” is just an attempt to try and correct for the inaccuracies of using hour meters to record air time or flight time.