If you are undetected and use a normal attack, it is the same as oblivion. If you use a power attack, you preform an assassination move. High and Low profile depend on the weapon (can't knife a guy with a hammer)
High Profile Weapons: Longsword, Hammers, Axes
Low Profile Weapons: Daggers, Shortswords, Arrows (stab them, not shoot)
As for a bow, maybe a High Profile and you strangle them with the string?
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High Profiles will alert anyone nearby as the target will cry out for help. Low Profiles make the body drop down quietly.
Morrowind's Remove Corpse should return too.