Paired cards always count, so in the absence of straights and flushes a hand of five different ranks always beats a hand containing any duplicate ranks. The differences depend on whether Aces are counted as high or low, and whether straights and flushes count.
The different possible rankings for low poker are explained on the hand ranking page. They differ in the hand ranking, the drawing procedure and whether a wild card is used. On this page several versions of this game are described. Most poker variants can be reversed in this way, but the name 'Lowball' is most often used to refer to a low version of Five Card Draw Poker. Lowball or Low Poker is poker in which the lowest ranking hand wins.
