They are talking about H.R. 2640. They don't mention that it's supported by the NRA, but they are more accurate than the NRA, in calling it a "gun control" bill.
Expect to see the changes desired by "Several groups, including the Coalition to Stop Gun Violence, the Violence Policy Center and the Legal Community Against Violence" to be made by the Senate, and quietly passed by the House, by voice vote at 0-Dark thirty, when the changes are sent back to them. After all the NRA supports the bill, right, what could be a safer vote?
I wouldn't bet on that. Schumer has said in effect that he is balls to the walls against changes. I doubt the NRA would go for it. That would mean a conference committee. Blue dogs in the House won't stand for that. It would probably force a recorded vote in the House.