Time is running out.
This expression means that the time limit is very close. Soon we will have no time to do something.
“The spring auto sale will end in 3 days. If I want to get a good price I have to buy a car soon, time’s running out!”
This expression means there is no time left to do something. You don’t have any time left. (to do something)
“Time is up for the quiz! Please stop writing and hand in your tests.” = You have no more time for the test. You have reached the limit.
* Time’s = Time is