The House passed a bill called HR 3590, the Service Members Home Ownership Tax Act of 2009, which had nothing to do with healthcare. And then the Senate put their version of the ACA as an amendment to that bill.
EDIT: The House bill and the Senats bill were pretty similar, but if you want to know their differences, there's a pretty comprehensive listing of the differences here: www.nytimes.com/interactive/2009/11/19/us/politics/1119-plan-comparison.html
There were basically three major changes between the two bills:
Some moderate Democrats in the Senate like Joe Lieberman were against the public option (because they thought it would weaken the private insurance market), so the Senate bill removed the federal public option that was in the House bill, although it did give states the choice to create their own public options (which is how Vermont was able to institute its single-payer healthcare plan).
The House bill included the Stupak amendment, which prohibited any Federal subsidies being used to buy insurance policies that covered abortion (although you could still attach a rider to your policy that would cover it). But a lot of pro-choice Senators found that too restrictive, because it might have led insurance companies to simply decide not to offer any policies at all that cover abortion. So the Senate bill said that people receiving Federal subsidies COULD buy insurance that covered abortion, they would just have to segregate the funds, i.e. write one check with their own money to pay for the abortion part of the insurance, and write another check paying for the non-abortion part of the insurance using the Federal subsidies.
The Senate bill added a tax on Cadillac health plans, i.e. insurance policies that offered really generous benefits, to help pay for the cost of the bill.
Note that you shouldn't assume that whatever was in the Senate bill is now the law of the land. You see, after the Senate bill was passed by the Senate, Ted Kennedy died, and the Democrats lost their filibuster-proof majority in the Senate when Republican Scott Brown replaced Ted Kennedy. So the only way to make Obamacare into law was for the House to pass the Senate bill. But the House didn't like some of the things that were in the Senate bill, so what they did was pass the Senate bill, which then became law, but then they passed a new bill to make changes to the Senate bill, through a process known as budget reconciliation which bypasses the filibuster. The new bill passed through reconciliation made two significant changes:
It weakened the individual mandate and the enforcement of the mandate, since House Democrats were less supportive of the mandate now that the public option had been removed.
It delayed the tax on Cadillac health plans (I don't remember the time period of the delay), since House Democrats were reluctant to impose a tax that would have impacted a lot of union workers.
There was also one other significant change relative to the Senate bill, although it was not passed legislatively: Bart Stupak and his fellow pro-life Democrats in the house didn't like the changes the Senate had made to the abortion provision, because they argued that money was fungible, so even if you wrote two separate checks, the government would still be paying for your abortion coverage, because by paying for some of your healthcare expenses, it would leave you with more money to pay for abortion coverage. So as the price of agreeing to pass the Senate bill, those House members got President Obama to issue an executive order stating that no Federal money could be used to pay for abortion coverage, just like the Stupak amendment in the House bill said.