TARP1 was Paulson's plan (which had to be passed within days, you may recall, to avoid financial Armageddon), in which we needed to spend $700 Billion to purchase toxic assets from financial houses. Congress gave him half that amount and then became confused and angry when he didn't use it to buy up toxic assets. He told them that he had decided that buying toxic assets actually was not going to work.
TARP2 is Geithner's plan in which we need to spend $700 Billion $1 Trillion or more to rename toxic assets as "legacy loans" and give money to hedge funds so that they can buy these legacy loans from financial houses. Apparently buying up the toxic assets from financial houses will work fine if we first rename them as "legacy loans" and do it through an intermediary.
Bear in mind that I didn't go to college, so I may have it wrong.