Need verification of real-time concepts
Yes, your understanding is correct. Real-time software must respond by a deadline. It may also need to implement accurate time delays (e.g. a traffic light controller). It must be deterministic in its time behaviour as well as its logical behaviour.

Note that this standard definition of "produces results by a deadline" could also be applied to some business software, e.g. payroll! The payroll program must produce results by a deadline, i.e. pay-day! But we don't normally think of payroll as a real-time program. Typical business payroll programs are not written as real-time, deterministic software.