"Real time" is defined in terms of deadlines, a system is real-time if operations have specific deadlines, times they take to execute.
The level of real-timeness is what happens when an operation misses its deadline:
* In a hard real-time system, missing a deadline is total system failure. Deadlines tend to be tight, and system correctness or integrity may not be maintained in the face of a missed deadline. Rocket guidance systems for instance, if a process misses its deadline the rocket can veer off-course or blowup or abort or…; other examples of hard real-time system are engine controls or medical devices.
* In a firm real-time system, missed deadline leads to QoS degradation, and the result of the operation is ignored/discarded after a deadline miss. Manufacturing systems tend to be that, missing deadlines will usually ruin parts (possibly for some time afterwards), but the production can usually recover and continue.
* Soft real-time are a relaxation of firm, where the result of the operation is still valid after a deadline miss, but its value usually diminishes as the deadline recedes into the past, real-time audio transmission (phones & stuff) is usually there: you want your audio to be delivered "immediately" but can still use it if there's a small delay (missed deadline), however as delay increases delivering the data becomes less and less useful e.g. a few hundreds milliseconds delay on a phone line is annoying, a few minutes makes it useless.
hard vs. soft real time is a matter of latency tolerance. human-facing systems (like telecom) need to be low latency from a human perspective, which is a higher threshold than what you could tolerate in a mechanical context where 100ms could mean damaging some expensive hardware.
