What Jim said... the smoke ring is decorative and in scientific terms, oxygenated myoglobin (that pink/red stuff a lot of people think is blood). The smoke contains nitrogen dioxide and is responsible for mixing with the meat to create this coloration (actually, lack of coloration). Believe it or not, the amount of smoke your meat has absorbed has nothing to do with this ring. But it's very pretty looking. :)
With that said, any time you burn organic material, aka wood, you will produce nitrogen dioxide which will start the creation of a smoke ring.