GWEN IFILL: Now we continue our series on issues shaping this election.
Tonight, we focus on guns.
John Yang reports.
JOHN YANG: In their first debate, a rare moment of harmony, as the two presidential candidates actually agreed on a highly contentious subject: guns.
HILLARY CLINTON (D), Presidential Nominee: We finally need to pass a prohibition on anyone who's on the terrorist watch list from being able to buy a gun in our country. If you're too dangerous to fly, you are too dangerous to buy a gun.
DONALD TRUMP (R), Presidential Nominee: I agree with you. When a person is on a watch list or a no-fly list — and I have the endorsement of the NRA, which I'm very proud of. These are very, very good people, and they're protecting the Second Amendment.
But I think we have to look very strongly at no-fly lists and watch lists.
JOHN YANG: But that's where the agreement ends. Donald Trump is running as a strong defender of gun rights and says Hillary Clinton wants to take guns away.
Last month, Trump said, if Clinton wants to restrict access to guns, she should start with her Secret Service detail.
DONALD TRUMP: I think that her bodyguards should drop all weapons. They should disarm, right? Right? I think they should disarm immediately. What do you think? She doesn't want guns. Take their — let's see what happens to her. Take their guns away.
JOHN YANG: The National Rifle Association is running ads supporting Trump.
NARRATOR: She keeps a firearm in this safe for protection. But Hillary Clinton could take away her right to self-defense, and, with Supreme Court justices, Hillary can.
JOHN YANG: Clinton says she just wants tougher gun control.
HILLARY CLINTON: I'm not here to repeal the Second Amendment. I'm not here to take away your guns. I just don't want you to be shot by someone who shouldn't have a gun in the first place.
JOHN YANG: She vows to expand background checks for gun buyers by closing the Internet sales and gun show loopholes, using executive orders if Congress won't act. After the Pulse nightclub shooting in Orlando, Clinton doubled down.
HILLARY CLINTON: I believe weapons of war have no place on our streets.
HILLARY CLINTON: And we may have our disagreements about gun safety regulations, but we should all be able to agree on a few essential things.
JOHN YANG: Clinton has used urban gun violence to give urgency and a human face to her call for stricter gun control. Earlier this year, she spoke at a fund-raiser for the Circle of Mothers, a group that supports women whose children have been killed by gun violence.
This week, she spoke about the issue at a black church in Charlotte, North Carolina.
HILLARY CLINTON: We have to fight for commonsense reforms to stop the epidemic of gun violence in our communities.
HILLARY CLINTON: Gun violence is by far the leading cause of death for young black men, more than the next nine causes combined.
JOHN YANG: Adam Winkler is a UCLA Law professor.
ADAM WINKLER: All of Secretary Clinton's proposals are at the very top of the gun control agenda, universal background checks, restrictions on assault weapons, and things like a no-buy list for terrorists.
JOHN YANG: Trump opposes restrictions on assault weapons and increased background checks. He says if a gun owner has a permit to carry a concealed weapon, it should apply nationwide.
ADAM WINKLER: It would effectively mean that a state that has the easiest, loosest, most permissive carry laws will set the laws for the entire nation. This would be a radical reform of America's gun laws, undermining states' right and lead to far more people carrying guns.
JOHN YANG: Immediately after the Pulse nightclub, Trump said more guns would have helped.
DONALD TRUMP: If you had some guns in that club the night that this took place, if you had guns on the other side, you wouldn't have had the tragedy that you had.
JOHN YANG: After the Sandy Hook school shooting, Trump tweeted that President Obama's call for stricter gun control spoke for him and every American. Now Trump wants to eliminate gun-free zones around schools and parks.
The fate of either candidates' proposals is likely to rest with whoever controls Congress. So, no matter who wins the White House in November, the battle over gun control isn't likely to end.
For the "PBS NewsHour," I'm John Yang.