When the House and Senate pass different versions of the same bill, someone has to reconcile them. That happens in a conference committee, sometimes called the third house of Congress.
A conference committee is a temporary joint committee of members from both the House and the Senate, created to resolve the differences when each chamber has passed its own version of the same bill. The two versions cannot both become law; the committee hammers out a single compromise.
It exists because of bicameralism. Since a bill must pass both chambers in identical form before going to the president, and the House and Senate often pass different versions, there must be a way to merge them. The conference committee is that way.
Its power is considerable, and a little hidden. The conferees can make significant changes as they reconcile the two bills, and the compromise they produce, the conference report, then goes back to both chambers for an up-or-down vote, usually with no further amendments allowed.
This is why it is sometimes called the third house of Congress. A small group, meeting late in the process, can shape the final form of major legislation, with the full House and Senate left only to accept or reject their handiwork whole.