Time was historically measured by the number of lunations, seasons, or days. The tax for the last harvest was sometimes due when the next one bloomed.
With the advancement of technology and the invention of the first mechanical clocks, which at the very beginning the purpose was simply to continue to give the time when the sun was no longer shining on the sundials, more precision arrived. The clocks at the beginning equipped with only one hand, that of the hours, received a hand more with that of the minutes followed by that of the seconds.
Other timepieces arrived, the marine chronometers, mounted on gimbals to remain always horizontal and thus increase the precision, allowed the navigators to calculate their position at sea with precision. Then came pocket watches and then wrist watches. The arrival of tuning-fork watches, quartz watches, and then radio-controlled watches increased the precision of timekeeping. Nowadays the main units to measure time are not really the number of moons but rather the number of days, hours, minutes and seconds.
On a larger scale there are still some different calendars used in the world to measure time. The most used is a solar calendar, the Gregorian calendar. We also have the Hebrew calendar, which is a lunar-solar calendar, or the Hegerian calendar which is a lunar calendar.