"Soft realtime" means it operates in real-time, able to land exact guarantees within given time constraints reliably; "Hard realtime" means it's able to make 100% perfect guarantees within given time constraints, and absolutely will not miss those guarantees. "Soft realtime" requirement means your shit only operates if realtime works, but it's okay if realtime fails--it can recover, or if it flat out fails out it can be restarted with no harm. "Hard realtime" requirements mean a failure is CATASTROPHIC and has SEVERE CONSEQUENCES.
Okay, I admit I forgot about one thing: the definition of hard- and soft-realtime can be context specific. In the multimedia world, soft realtime would refer to something like realtime 3D rendering in games and visualizations, where a frame does not strictly have to finish rendering until a certain deadline is met; instead, there is a tolerance range for the interval of each rendering (and for how fast and how much this interval changes over time). Audio is hard realtime, because even one missed sample is an error (in case of capturing, arguably fatal, because it can mean the entire recording has to be thrown away). In your definition, all of them would be lumped together in the "soft realtime" category, which is not really useful.