What is the difference between'time is up' and 'time is over'

"Time is over" seems to refer to time as a period that has passed. "Time is up" seems to refer to time as a certain deadline that has been reached. So when one says that the time to submit applications is over, it means that the opportunity to submit an application is missed, and when one says that the time is up, it means that you should submit your application ASAP, since it is your last chance.

I think 'time is up' is more recent, more immediate and so tends to refer to the moment of reaching a deadline or soon after i.e. still relevant, while 'time is over' is more broad and general and so tends to refer to a period of time that is in the past and not of current relevance. The immediateness of 'time is up' is what I think gives it its relative abruptness and so its negativity in some contexts.

They both express the same essential meaning: A period of time has ended.

The connotations of the two are slightly different. "Time's up" is very similar to the phrase "time's run out." It conveys an environment where time is a limited resource and someone is attempting to accomplish a particular task before the resource is used up or runs out.

Time's up! Put your pencils down and pass your exams forward.

I barely finished my exam before time was up.

"Time is over" signals the end of a longer period; one that could have conceivably lasted forever. If it is associated with a deadline for a particular task than the deadline is not typically rushed -- the allotted amount should be more than enough time to complete the task.

This usage is very similar to phrases such as "time has ended" or "time has gone" or even "from another time."

The time for joking is over.

Put away your disco clothes; that time is over.

Now that the ruler has died, this dynasty's time is over.