Utility Rope, Life Safety Rope
Utility rope is essentially any rope used for a purpose that does not involve supporting the weight of a human being. It must not be used as a life safety rope for any reason. Typically, you'll see these used to hoist tools, as a ladder halyard, or for stabilizing something. Despite the fact that they are not used for life safety, they still must be inspected regularly. A lot of fire departments make it easy to determine which type of rope you have with color codings or markings.
Life Safety Rope is any rope that is designed for and used in situations that the weight of one or more person must be supported. It must not be used as a utility rope for any reason. Life safety rope comes as a one person rope or a two person rope. For general safety, "one person" is considered to be 300 pounds. In stride with that idea, a two person rope is rated at 600 pounds. Any life safety rope must be inspected after every use. EVERY. USE. Once a rope fails an inspection, it cannot be used as a life safety rope again. Life safety rope is also required to be of block creel construction, and made with continuous filament virgin fiber (all that means is that it has never before used, and is not spliced together).
Lastly, a personal escape rope follows similar criteria to the life safety ropes. The only true difference is that is designed to be used only one time, and intended for situations in which a firefighter needs to self-rescue from a bad situation as quickly as possible. Of course, a properly trained firefighter should never need this, but there's a reason we have a Murphy's Law section of this site. Once used, it should be replaced. These ropes will fit in the pocket of your turnouts easily, and should be long enough to tie off to a stationary object and have enough remaining slack to let you hang out a window. Sounds like fun, right?
Before I move on, a quick note on shock load. Putting a ton of weight on a rope very rapidly is a great way to ruin it. Sometimes this can't be avoided, but the rope record should denote any time a shock load has been applied to a piece of rope.
For more info, rope requirements for fire departments can be found in NFPA 1983.