Tach hour recording (odometer) measures correctly with respect to time at maximum RPM. It has nothing to do with throttle position or the power the engine is producing; only with RPM. Operate at a lower RPM, the tach is turning slower, and it's recording time more slowly. It's strictly a mechanical function of the instrument. Turn the instrument faster, the time turns over faster. This is a good measure of the work the engine is doing, and consequently a good way to keep track of time for maintenance purposes.
Datacon and Hobbs are simply brand names of electronic hour meters. When they begin recording time depends on the installations. Some begin when the battery master relay is energized, some when the engine oil pressure activates a pressure switch to start meter. Others are attached to landing gear squat switches, or pressure switches that activate when enough parasitic drag develops as airspeed increases.
Generally billing is done by the electronic meter, while maintenance is scheduled by the tach.
If you're rushing your checklists to save a dollar (or euro or pound as the case may be), then you're flying under the wrong set of priorities.