A burned valve is literally burned; ie it will have a portion of the seating surface burned/melted off. It's junk, high quality scrap. Burned valves are caused by a)lean fuel mixture, too much air not enough fuel. Possible culprit, vacuum leak, improperly matched intake/exhaust system, b)too much spark advance, c) a combination of the two. There are other causes but these are the most common.
Carbon build-up is just that nothing else. Provided the valve is within specifications(straight, stem not worn, enough face to be resurfaced) it should be used again. Valves don't need to be replaced in sets. The only advocate of replacing sets is the guy selling the set.
There are no chemical cleaners I would recommend to remove carbon build up from a valve. However, if you want to remove carbon from a running engine that's a different story. Have a friend bring your car to a high idle and with the air cleaner removed squirt small amounts of water into the intake tract. The water will turn into steam inside the combustion chamber. The resulting steam "explosion" with loosen the carbon. The engine operation will blow the carbon out of the cylinder then the exhaust. I've done this with good results. A word of caution. Do this outside and make certain no one is standing behind the exhaust. I've seen good sized hot chunks of carbon whizz out of the exhaust!
Best way to remove the bulk of carbon is with a wire wheel. Wear eye protection when cleaning the valve with a wire wheel as the wires tend to fly of the wheel and embed themselves into whatever. Final cleaning is best done with a media blaster.
Have the valves and seats cut(resurfaced) by a professional. It will be cheaper in the long run. Remember, you never have the time or money to do the job right the first time! Take it from a guy who has screwed up and been screwed in every possible automotive process. Learn how to do repairs yourself or find a wrench you can trust.
Lapping valves with grinding compound is an old technique. Modern automotive machinists haven't lapped valves in decades. However, in a pinch it can be done but the results will be sketchy at best. Lapping a valve is inaccurate. The process "follows" the existing contours of the seat and valve. Where as modern techniques cut the seat and valve to the proper angle.
A modern "performance" valve job will use as many six angles to maximize air flow(efficiency). Which results in better gas mileage and more power.
Remember, this is a simplification of the "valve job" process and theory. The head of an internal combustion engine can make or break its reliability, efficiency and performance. Unfortunately it's dumb; it can only do what you make it.
Happy Motoring!!!