This MTG Duels of the Planeswalker is a single player game where you go through levels with a boss fight at the end. Each level is a game and same with the boss. This one just has some DLC, no buying boosters or anything.
MTG Online is a totally different game. It is suppose to be like MTG but online, you have to buy digital booster packs and such for that.
there is online multiplayer in this game though. These games are an excellent way to learn to play since you have the game to automatically tap, untap, keep track of health, easily discern flyers from non-flyers, etc. there's also puzzles where a situation is set up and you're given a specific hand and you must try to figure out how to meet X conditions. usually it's you have to figure out how to win that turn.
in online multiplayer you can play 1v1 or two headed giant (2v2) or free for all with up to 4 players.
you unlock cards by winning matches... either against the computer in the campaign mode or through wins online.
overall... i'd say if you've ever had an interest in mtg... or wanted to try and convince a friend to play mtg... it's totally worth the $4 or whatever to see if it's something you'd like. it's certainly the cheapest way to buy in