It's confusing but let's see what we can do to clarify;
Old(er) aircraft may not originally have or have had a Hobbs meter.
Installing can be costly as it needs to be wired into the electrical system and tapped into the oil pressure line. Yes a true Hobbs meter runs on oil pressure and not on the Master switch on.
If you accidentally leave the master switch on or take 10 min to read a checklist with the Master switch on the Hobbs should not run.
If it does then it's only wired into the electrical system.
So Hobbs time should be true engine run time and is for all intends and purposes (by the FAA) legal to log as flight time in your logbook although operating time is probably a better word.
A Tacho runs even with clock time at a high powers setting.
So if somebody comes back after an hour clock time with 1.0 Tach time they've run it balls to the wall.
Anything less then (almost) full power the tach runs slower then clocktime.
In normal flight training operations this is usually a factor of 1.25 meaning that one hour of Tach is really 1hr 15 min of engine run time.
0.8 Tach is around one hour clock time.
So if the school or club charges by Tach and Tach only they're basically robbing themselves because fuel is still being burned, instructors are still providing their time and wear and tear and depreciation is still taking place.
So lets say the airplane is $100/hr and the instructor is $50/hr and the school uses teh Tach:
1.0 Tach = 1.25 x$100 + 1.25 x $50 = $125 + $62.5 = $187.5
This would not include briefing and debriefing time for which the instructor needs to be paid. So let's say 15 min pre and 15 min post for another $25.
Final bill $212.5 and you expected $150 because you don't know how the billing works.