My current operating theory is that stardates are an invention of Starfleet Command and provided for in the Articles of the Federation. The purpose of stardates is to provide a means of the entire fleet, and eventually basically all civilian traffic, to coordinate actions throughout the galaxy.
Since Starfleet Headquarters are on Earth, in the Pacific Time Zone, stardates are based on Earth time. One "stardate" would be equal to one eight hour duty shift in San Francisco. So, 5937.0 might be 08:00 at SFHQ and 5938.0 would be 16:00 at SFHQ. Every 0.1 stardate equals 48 minutes on Earth. This means 1000 stardates equals 333 days and 8 hours. Or, a bit over 11 months. So, nearly a year.
Stardates are calculated by computers throughout the Federation and all ships and bases use this as a standard. However, due to relativistic time distortion (which is negated to some degree during warp-flight, but not in other times) the apparent passage of time may be different depending on your position in the galaxy, your velocity, and who knows how many other factors. So what equals 48 minutes on Earth may be 59 minutes or 33 minutes or whatever in other locations and under different conditions. Ships still have their own local time and that would be basically unique from ship to ship and from base to base. This local time proceeds apace at one hour at a time relative to the time experienced by the crew. So, any given hour or day of the week will likely not match any other ships's, but the stardate will be exactly the same. Notice, DS9 uses Bajoran time, but still uses stardates. Because ships move around and constantly are changing their velocity and their location in the galaxy, the proportion of local time for the ship experienced by the crew is constantly changing compared to the passage of stardates. So, stardates will seem to speed up or slow down. To the crew, stardates would seem to be of variable length, and the hours and minutes would seem steady, while, in fact, their hours and minutes are variable and the stardates are universally constant.
The stardate is the absolute time that everyone in the Federation can agree to. Stardate 47988.3 is 47988.3 throughout the galaxy.
As for other uses, yes, I assume the UT translates foreign time increments to either stardates, if it knows the conversion, or a more traditional type of date description if there's no way for it to know what stardate that would have been.