Do planes have odometers?
A Hobbs meter measures the time spent in a general aviation aircraft with the power on.

Planes differ in that time is easier to record than distance. For a given airspeed, the distance covered by the aircraft depends on the wind, altitude, and other factors.

Modern airliners would record the period each engine has run, flight time, cycles (one cycle is one pressurization/depressurization cycle), etc., digitally.

Those records are then used to track the time between overhauls (TBO). Same as with cars.

For small planes, a tach timer is used to record the revolutions the engine has made, this one is used for TBO.



(Source) Image of tach timer.