Just to make it a little more clear, the House bill and the Senate will will have to be passed. Then a committee will be formed to take up the bills and compromise to make both bills read the same. This involves both sides to make concessions. The added amendments will also have to be ratified along with the two bills. Once the commttee finally agrees on ONE bill it then goes back to the House and Senate and they vote on the new bill. If both the House and Senate pass the bill, it is sent to the president to sign. If he signs the bill, it then becomes law.
I haven't gone through the entire process, but this is about it.
Jim Smith