There's two kinds of killstreaks that I've noticed. Quick killstreaks, and overall killstreaks. A quick killstreak is getting an amount of kills within a few seconds of each other without dying, sort of like a chain. Overall killstreaks are just how many kills you've gotten without dying, period.
Quick killstreaks, which I like to call killchains, are harder to obtain due to the fact that there have to be enough people grouped up to equal the amount of kills in said killchain, and you have to be fast and skilled enough to take them all out within seconds of eachother. Overall killstreaks are way easier to obtain because they have no time limit before the streak expires.
My highest killchain is overkill, which I believe is 6 or 7 kills. My highest overall killstreak is Beyond Godlike. I can verify that this is the highest one due to having quite a few perfect games, and not having anything else be shown. There is nothing beyond beyond godlike. Winning the game without dying, also known as getting a perfect game, does not give any special title afterwards.