Sometimes the difference depends on what sort of shooting or training is taking place at a range, and/or who is conducting it.
Civilian ranges often must worry about liability, and their insurance policies might dictate what is and is not acceptable.
Military ranges, for example, are not required to be concerned about some of the issues that civilian ranges must be aware of.
Quite often, on a range (or set of ranges) that may have more than one firing line - it is the LINE that is called "hot" or "cold", to allow shooters to inspect their targets, deal with some malfunction, etc.
The firing line for a course of fire, generally run by range safety officers (who may have different names in different environments), can often be "hot" or "cold" independent from whether a range is designated as a "cold" range or "hot" range.
Knowing the rules of any range you are on is the responsibility of the shooter, and the fact that the rules are different on different ranges makes it worth your while to ensure you familiarize yourself with the rules whenever you find yourself on a range you've never been to before.
Treat everyone you meet with dignity and respect....but have a plan to kill them just in case.