Magic: the Gathering Online is for players who want to play the hobby online. It has, to my knowledge, most if not all sets on there for playing. Think of it as real online Magic - you collect cards, build decks, and play against other players.
Magic: the Gathering - Duels of the Planeswalkers, on the other hand, is a game with prebuilt decks, a group of AI opponents to play against (in normal games and an Archenemy campaign), and a vague storyline to follow. The decks can't be significantly altered, but can be improved with cards that you win through the campaign.
In short: Online is Magic Online. Duels of the Planeswalker is Magic: the Video Game.
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