Differences between fired and unfired pressure vessels?

Fired pressure vessels are a separate category of vessels that include power boilers and other vessels that are designed to accept heat. This category of component would include coal/gas and oil fired boilers and well as boilers that are heated by a waste heat gas stream or a hot oil system. Electricly heated steam generators are also considered to be "fired"

"Unfired" pressure vessels are almost everything else that is pressurized to 15 psig or higher. This would include things like pressurized tanks storing air, nitrogen, ammonia or natural gas.