JUDY WOODRUFF: It's the debate day after, and the two presidential candidates have decidedly different takes on how things went.
John Yang begins our coverage with this report.
JOHN YANG: Twelve hours after stepping off the debate stage, Hillary Clinton was back on her campaign plane sounding upbeat.
HILLARY CLINTON (D), Presidential Nominee: Well, we had a great, great time last night. The real point is about temperament and fitness and qualifications to hold the most important, hardest job in the world. And I think people saw last night some very clear differences between us.
JOHN YANG: Clinton said some of Donald Trump's debate statements were demonstrably untrue and dismissed one of his grievances about their face-off.
HILLARY CLINTON: Anybody who complains about the microphone is not having a good night.
JOHN YANG: Trump told reporters after the debate that his mic was defective and suggested it was on purpose. He also claimed that moderator Lester Holt of NBC News was tougher on him than on Clinton. Trump insists he came out ahead anyway.
DONALD TRUMP (R), Presidential Nominee: I was asked about my tax returns, which I have told about 500 times. I think I did really well in answering those questions, but those questions are not answerable in a positive light.
JOHN YANG: Last night, Clinton opened up a new front in the battle for women's votes. At the end of the debate, she spoke of the case of a former Miss Universe.
HILLARY CLINTON: He loves beauty contests, supporting them and hanging around them. And he called this woman "Miss Piggy." Then he called her "Miss Housekeeping," because she was Latina. Donald, she has a name.
DONALD TRUMP: Where did you find this? Where did you find this?
HILLARY CLINTON: Her name is Alicia Machado.
DONALD TRUMP: Where did you find this?
HILLARY CLINTON: And she has become a U.S. citizen, and you can bet…
DONALD TRUMP: Oh, really?
HILLARY CLINTON: … she's going to vote this November.
DONALD TRUMP: OK, good.
MAN: You are the new Miss Universe!
JOHN YANG: The Clinton campaign quickly released a Web video of Machado, a Clinton supporter, criticizing Trump.
ALICIA MACHADO, Former Miss Universe: "Hello, Miss Piggy. Hello, Miss Housekeeping."
JOHN YANG: This morning, the Republican nominee fired back on FOX News.
DONALD TRUMP: She gained a massive amount of weight. And it was a real problem, not only that, her attitude. And we had a real problem with her.
MAN: Good afternoon, Miami.
JOHN YANG: This afternoon at a town hall meeting with Latinos in Miami, Trump mentioned the debate only briefly.
DONALD TRUMP: It was an interesting evening, certainly, and big league, definitely big league.
JOHN YANG: In North Carolina, an energized Clinton relived a memorable moment from the debate.
HILLARY CLINTON: At one point, he was kind of digging me for spending time off the campaign trail to get prepared. And I said, yes, you know what, I did prepare. And I will tell you something else I prepared for. I prepared to be president of the United States, and I think that's good.
JOHN YANG: Early ratings show that more than 81 million people tuned in last night, a record for a presidential debate.
For the "PBS NewsHour," I'm John Yang.
JUDY WOODRUFF: We will take a closer look at some of last night's debating points and hear from a representative of each campaign after the news summary.