The assumption is, that language which is identical in each version will stay as is. No language will be added if it didn't come out of either bill. The Conferees will only deal with items which are in one version but not the other.
Like so much of what goes on in the Congress these rules are, as they say, largely honored in the breech.
Language which is identical in both the House and Senate bill is often changed (or deleted) by the Conferees. Language which does not exist at all, is often inserted by the Conferees (this is where much of the "earmark" skullduggery takes place). Language which is in one bill but not the other might just be dropped altogether as the agreements, swaps, deals, and trade-offs are worked out.
At some point the Conferees (and their staffs) will agree on the text of the bill and produce what is known as a "Conference Report." This is the agreed-upon language and goes to each chamber for an up-or-down vote. Conference reports are not amendable.
Assuming both the House and the Senate agree to the Conference Report on any given bill, it is signed by the Speaker of the House and the President Pro Tempore of the Senate and trucked on up to the White House so the President can act on it.
If the President vetoes a bill, it takes a 2/3 vote of each Chamber to override that veto which doesn't happen very often.
The only other group which gets a say in this law-making biz is the Supreme Court of the United States. In the case of Marbury v Madison (1803) established the right of "judicial review." That means the Court can declare a law - or a section of a law - as being contrary to the Constitution and making it invalid.
I knew that because I actually attended most of Dr. Robert Hill's Con Law classes at Marietta College, Marietta, Ohio 45750.
That, class, is how a bill becomes law.