Republican presidential candidate, businessman Donald Trump waves has he arrives for a campaign rally Monday, Feb. 8, 2016, in Manchester, N.H. (AP Photo/David Goldman)

Tuesday night in New Hampshire, a state in which independent voters make up a large chunk of the electorate, Bernie Sanders and Donald Trump sailed to easy victory -- victories so thorough that the races were called as soon as the polls closed. Sanders basically tied with Hillary Clinton among Democrats, according to exit polling reported by CNN, but won independents by 50 points. Trump got about a third of the vote from Republicans and independents equally.

Independents, definitionally, operate outside the established party structure. They are independent of it, independent of the mandates and whims of the national committees, independent of the whole apparatus. And to an extent that is largely without precedent, so are the candidates who won on Tuesday night. Sanders, still considered an independent in the eyes of the Senate, is explicitly running against the Democratic Party as he raises huge sums of money from huge numbers of people. Donald Trump has completely emasculated the Republican Party in every possible way, sidelining it on endorsements, on debates, on fundraising, on everything.

It's particularly worth calling out that difference on money. While there are tactical similarities between the two, and while both are similarly positioned to appeal to voters frustrated with the political system, the arguments they make to differentiate themselves from that system are very different.

Here's part of Sanders's speech after his victory on Tuesday night.

"We have sent a message that will echo from Wall Street to Washington, from Maine to California," he said, "and that is that the government of our great country belongs to all of the people and not just a handful of wealthy campaign contributors and their Super PACs." He later continued: "I do not have a Super PAC, and I do not want a Super PAC."

"I am overwhelmed, and I am deeply moved far more than I can express in words by the fact that our campaigns financial support comes from more than one million Americans who have made more than 3.7 million individual contributions," he said. "That is more individual contributions than any candidate in the history of the United States up until this point in an election. And, you know what that average contribution was? 27 dollars."

At the end of his speech, he encouraged people to toss money onto that pile. His plea broke his campaign's website.

That's Sanders's revolution. The people joining to together and funding his run for the White House, allowing him to sidestep the established power structures on which Clinton relies.

Democratic presidential candidate Bernie Sanders addresses supporters after winning the New Hampshire primary. (Reuters)

Contrast that with this excerpt from Trump's speech.

"I think one of the thing that really caught on is very important, self-funding my campaign," he said, continuing, "I don't think people really appreciate it, because I see all of this money being poured into commercials, and it's not their money; it's special interests' money. And this is on both sides. This is on the Republican side, the Democrat side -- money just pouring into commercials."

"These are special interests, folks," he said. "These are lobbyists. These are people that don't necessarily love our country. They don't have the best interests of our country at heart. We're not going to let it happen. We can't -- we have to do something about it. When you see -- when you see the kind of deals made in our country, a lot of those deals are made because the politicians aren't so stupid. They're making them for their benefit. We have to stop it. We have to stop it. We are now going to make it for your benefit."

Republican presidential candidate Donald Trump addresses his supporters after winning the New Hampshire primary. (Reuters)

That's Trump's sales pitch: The party doesn't care about you because the lobbyists pay them not to. Trump will step in and knock them all back into place because he doesn't want and doesn't need their money at all. Trump spent months exaggerating the extent to which he is self-funding -- he raised millions in 2015 from individual donors -- but the outcome is the same even if the point is different. And it is that we must avoid money from big donors because the people (Sanders) or Donald Trump (Trump) should be the force for change.

This is a weird middle spot between the parties. Republicans and Democrats are typically both dependent on groups of big donors (with some overlap between those groups, too). Both Trump and Sanders reject that idea -- but Sanders rejects it because he advocates for a bottom-up campaign and Trump rejects it for a top-down one. In the same way that independents mostly fall into partisan groups, this 2016 independent electorate is lining up on the left or on the right depending on how the candidate on each side talks more broadly about how the presidency should work. Sanders constantly talks about the need for a populist upswell that he can use as a cudgel on Capitol Hill. Trump constantly talks about how he himself is the cudgel.

In the 18 hours since the polls closed in New Hampshire, Sanders's campaign reported on Wednesday, the candidate raised $5.2 million -- about half what Trump loaned himself in the entire fourth quarter of 2015.

Both candidates working outside the system -- in ways that drop neatly into ideological slots.