Korean chilli is a little different as it has a slight smoky flavour, in addition to being slightly sweet and also quite hot.
The actual name of the chilli use in kimchi and for that matter, most Korean dishes is gochugaru (고추가루). It comes in a variety of preparations, typically, finely ground, flakes and a paste.
You should be able to find this in most good supermarkets or an Asian store. If you can't get this, you can still use a good quality chilli powder or possibly, a paste.
There are a ton of different extraction methods used in the industry and it would be very difficult to pinpoint which one is used for a particular brand unless they tell you.
The "conventional", low-tech method is to use an alcohol solvent (capsaicin is alcohol-soluble; good thing to know in case you ever "burn" yourself with it). Very pure ethanol (grain alcohol) is probably the safest and what you'd use in a home extraction, although there are more effective solvents that are less safe such as acetone.
You grind up the dried chilies, let them sit in the solvent until it turns dark red, strain out the solids, filter the liquid remains, then evaporate the alcohol. That is a very simplified explanation, so do not try to actually do it yourself without a proper guide.
Manufacturing processes are much more precise. Solid Phase Extraction is one, Supercritical Fluid Extraction is another, there may be more. These are all highly purified (some claim 99% or better) which is far more pure than anything homemade.
So as to your question about what's in the bottle, the answer is: capsaicin. It's strange to ask if there are "any additives" because capsaicin is an additive. You cannot use that stuff as a hot sauce; you use it in minuscule quantities, i.e. one drop for an entire pot of chili. Of course, many brands of capsaicin extract are heavily diluted already (such as the "Pure Cap", which is only 500,000 SHU instead of the 16 million that actual pure capsaicin is).
It's easy enough to ascertain if it's diluted by just looking at the ingredients. Most will have an oil as the first ingredient. Not unhealthy, just filler. If capsaicin is the first or only ingredient, then it's pure.
Rest assured that a bottle of concentrated capsaicin is not going to contain significant quantities of anything more harmful than capsaicin itself. Even though it can't literally burn you, if it comes into contact with any part of your body, the reaction will be similar to that of a very serious burn. So don't worry about what else is in the bottle, worry about the capsaicin itself!
Best Answer
This is pretty much the same throughout the pepper family. The green chilis have "green" flavors - underripe, metallic, grassy. The ripe, red chilis develop more rounded, fruity flavors. You can just think of the difference between green and red bell peppers as a basic guide.