A walk down memory lane.
The concept of "real-time" dates back to the days of the mainframe.
Since processor time was so scarce, most processing was done in BATCH. That meant, you entered all your raw data at once through the operating system, indicated the program to be used for processing, and go to sleep. While you were in your bed, somewhere during the night, the processor would process your data all at once. When you came back next morning: lo and behold: the results.
Opposed to this was REAL-TIME. Some lucky SOB's were in the priviledged position to have enough access to the mainframe to be able to blow processor time on programs which handled input and output on the spot. It's not about response times per se.