Deterministic means that interrupt latency is constant, and doesn't depend on the system load. Here is the definition of the hard real-time vs soft real-time (from Wikipedia):
A system is said to be real-time if the correctness of an operation depends not only upon the logical correctness of the operation but also upon the time at which it is performed. The classical conception is that in a hard or immediate real-time system, the completion of an operation after its deadline is considered useless - ultimately, this may lead to a critical failure of the complete system. A soft real-time system on the other hand will tolerate such lateness, and may respond with decreased service quality (e.g., dropping frames while displaying a video).