(CNN) For Donald Trump and Hillary Clinton , the 2016 general election has all but begun.

The two presidential front-runners celebrated a victorious night Tuesday, each notching major wins in East Coast primaries and taking giant leaps towards their party's nominations. And in dueling victory speeches that showcased their starkly contrasting tone and style, Trump and Clinton had one thing in common: an eye on November.

Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates."Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey."

Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid. "I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid. "I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23."These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant."

Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House."So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement.

At a news conference at Trump Tower in midtown Manhattan, Trump declared that the GOP primary was "over."

"I consider myself the presumptive nominee," Trump said, as he blistered his two remaining rivals for making a deal to work against him. "Gov. (John) Kasich and Sen. (Ted) Cruz have really, really hurt themselves with a faulty deal that was defaulted on before it was even started."

"Whether you support Sen. Sanders or you support me, there's much more that unites us than divides us," Clinton said.

No one secured enough delegates to win the nomination of either party Tuesday. Still, the night marked a major turning point in a primary season that has already had plenty of twists and turns.

JUST WATCHED Super Tuesday in under 90 seconds Replay More Videos ... MUST WATCH Super Tuesday in under 90 seconds 01:23

Trump had a clean sweep of the five states where voters went to the polls: Connecticut, Delaware, Maryland, Pennsylvania and Rhode Island. CNN projected that the New Yorker would win all of the states before 9 p.m. ET -- a mere one hour after polls had closed. His dominance quelled -- though didn't snuff out -- talk that the nomination might be decided at a contested convention.

Clinton, meanwhile, defeated her rival in each state except Rhode Island -- the state the Sanders campaign had felt most optimistic about heading into Tuesday. It was also the only state that was an open party that allowed voters who aren't Democrats to participate in the primary.

JUST WATCHED The big delegate gains from Super Tuesday #4 Replay More Videos ... MUST WATCH The big delegate gains from Super Tuesday #4 04:22

The front-runners offered a preview of the personally charged, identity-politics battle that could come if they wind up in a general election clash. Clinton and Trump took aim at each other in their victory speeches Tuesday, and especially clashed on the issue of women.

When asked about Clinton by a reporter, Trump declared that the former secretary of state would make a "horrible president."

"If Hillary Clinton were a man, I don't think she'd get 5% of the vote," he said. "The only thing she's got going is the woman's card and the beautiful thing is, women don't like her."

Clinton addressed Trump's accusations head-on.

"The other day, Mr. Trump accused me of playing the woman card. Well, if fighting for women's health care and paid family leave and equal pay is playing the woman card, then deal me in," she said to a roaring crowd.

She also responded over Twitter.

Trump's clean sweep on Tuesday comes just days after Cruz and Kasich announced a joint effort to strategically divide some of the upcoming races to stall Trump's momentum. It also dealt a serious blow to the so-called "Never Trump" movement -- an anti-Trump faction within the GOP that's launched a campaign to stop the New York businessman from becoming the party's nominee.

"Even if the media yearns to declare this race over, the path to 1,237 delegates remains narrow for Trump, and he just left the most favorable part of the map for him in the northeast," the movement said in a statement.

If Cruz and Kasich are showing no signs of backing down, across the aisle, Sanders sent a more conciliatory message.

Although he told supporters in West Virginia that he polled better against Trump than Clinton, in a separate statement, the senator signaled that his primary goal moving forward would be issues and having a say in the Democratic platform.

"The people in every state in this country should have the right to determine who they want as President and what the agenda of the Democratic Party should be," Sanders said. "That's why we are in this race until the last vote is cast. That is why this campaign is going to the Democratic National Convention in Philadelphia with as many delegates as possible to fight for a progressive party platform."

Trump was more blunt in his triumphant speech surrounded by family and supporters and speaking to a throng of gathered reporters.

"As far as I am concerned it's over," he said.