"Do I consider myself part of the casino capitalist process by which so few have so much and so many have so little, by which Wall Street's greed and recklessness wrecked this economy? No, I don't."

It was a slow pitch over home plate for Sanders. There's no question he gets more often, no criticism he's better prepared for, than why he calls himself a socialist rather than a capitalist.

And then, in the debate's most interesting moment, Hillary Clinton jumped into the exchange.

"Let me follow up on that, Anderson," she said. "When I think about capitalism, I think about all the small businesses that were started because we have the opportunity and the freedom in our country for people to do that and make a good living for themselves and their families. I don't think we should confuse what we have to do every so often in America, which is save capitalism from itself."

Sanders didn't push the point:

"Everybody is in agreement. We are a great entrepreneurial nation. We have to encourage that. Of course, we have to support small and medium-size businesses. But you can have all of the growth that you want, and it doesn't mean anything if all of the new income and wealth is going to the top 1 percent."

This was the single most important exchange of the first Democratic debate — because it's the single most important cleavage in the Democratic Party today. Sanders's profession of agreement obscures a genuine divergence between the two candidates — a disagreement that reflects different views of the role that corporations should play both in the economy and in Washington.

Where Bernie Sanders and Hillary Clinton agree: Denmark is great

Sanders isn't a socialist. He's a democratic socialist. The difference is big, and it's real. When most Americans hear the word socialism, they think of something like the Soviet Union — a system characterized by the state owning the means of production.

But democratic socialism tends to describe the economies of Western Europe — vibrant, primarily capitalistic systems where the state tends to set more aggressive rules, and offer a more expansive safety net, than is true in the United States.

Sanders leans heavily on this comparison. When I interviewed him back in July, I asked him what it means to be a socialist, and he was quick to correct me. "A democratic socialist," he said:

What it means is that one takes a hard look at countries around the world who have successful records in fighting and implementing programs for the middle class and working families. When you do that, you automatically go to countries like Denmark, Finland, Norway, Sweden, and other countries that have had labor governments or social democratic governments, and what you find is that in virtually all of those countries, health care is a right of all people and their systems are far more cost-effective than ours, college education is virtually free in all of those countries, people retire with better benefits, wages that people receive are often higher, distribution of wealth and income is much fairer, their public education systems are generally stronger than ours.

During the debate, Sanders echoed that theme. "We should look to countries like Denmark, like Sweden and Norway and learn from what they have accomplished for their working people," he said.

Clinton wasn't having it. "We are not Denmark," she replied. "I love Denmark. We are the United States of America, and it's our job to rein in the excesses of capitalism so it doesn't run amok."

But this is a dispute that obscures deep similarities. Clinton and Sanders both want to make America look a lot more like Denmark — they both want to pass generous parental leave policies, let the government bargain down drug prices, and strengthen the social safety net. Their disagreement isn't over whether America should look more like Denmark.

Where Bernie Sanders and Hillary Clinton disagree: big business

The theme running through Sanders's political platform and his rhetoric is a deep and abiding skepticism of the role large corporations play in American life. This is core to his advocacy for single-payer health care, to his proposal to base pharmaceutical innovation around public prizes rather than private profits, to his plan to get big money out of American politics, to his opposition to private prisons, to his promise to break up the biggest banks, and more.

All those policies are driven, in part, by the fact that Sanders fundamentally mistrusts big businesses — he believes their most crucial innovations often simply free-ride on publicly funded research, he worries that their massive profits allow them to buy off politicians and rig the system for themselves, and he thinks they have too much power to squeeze worker pay in order to pad the coffers of executives and shareholders.

Which isn't to say Sanders is mistrustful of all businesses. In his riposte to Clinton, he stated his position carefully. "Of course, we have to support small and medium-size businesses," he said. The issue isn't private enterprise so much as it is bigness, and the power that comes with it.

Clinton doesn't share Sanders's mistrust. Her health-care plans have always envisioned a big role for private insurers, her trusted advisers include corporate executives, her Wall Street reforms leave large banks intact, and her history as a fundraiser displays a mastery of working with corporate titans rather than a rejection of their political role.

During the 2008 campaign, Clinton was asked why she keeps taking money from lobbyists. She responded in a way Sanders never would — with a defense not just of lobbyists, but of corporate lobbyists:

You know, a lot of those lobbyists, whether you like it or not, represent real Americans. They actually do. They represent nurses. They represent, you know, social workers. They represent … yes, they represent corporations. They employ a lot of people. The idea that somehow a contribution is going to influence you — I just ask you to look at my record I have been fighting for the same thing, my core values have not changed. But I do want to be the president for everybody. And I want to represent the entire country. And that’s what I’m aiming to do on my campaign."

Clinton believes big businesses are major, positive contributors to American life — they have their excesses, sure, but they drive important innovations, they employ huge numbers of Americans, and they deserve a seat at the political table. Her record as a policymaker shows that her instinct isn't to use the government to replace the services corporations provide but to use the government to help make sure everyone can afford those services, and to make sure the profit motive doesn't lead to abuse.

New Democrats versus Old Democrats

Clinton walks in the tradition of her husband and President Obama, both of whom emerge out of a post-Reagan strain of Democratic thinking that sees the private sector as vastly more efficient than the public sector. As Obama wrote in The Audacity of Hope:

[T]he conservative revolution that Reagan helped usher in gained traction because Reagan's central insight— that the liberal welfare state had grown complacent and overly bureaucratic, with Democratic policy makers more obsessed with slicing the economic pie than with growing the pie — contained a good deal of truth. Just as too many corporate managers, shielded from competition, had stopped delivering value, too many government bureaucracies had stopped asking whether their shareholders (the American taxpayer) and their consumers (the users of government services) were getting their money's worth. Not every government program worked the way it was advertised. Some functions could be better carried out by the private sector, just as in some cases market-based incentives could achieve the same results as command-and-control-style regulations, at a lower cost and with great flexibility.

But that tradition is under assault now. The basic argument of the post-Reagan Democrats was that unleashing the private sector would lead to more growth, more growth would lead to rising incomes for all, and higher taxes on the rich would buttress a safety net necessary for the very poor.

Many liberals now believe that unleashing the private sector led to the 2008 financial crisis, that the gains of growth are being captured by the top 1 percent, and that the only way to pass and sustain the high taxes on the rich needed to fund a sufficient safety net for the poor is to force big money out of American politics.

Sanders comes out of an older Democratic tradition — the tradition that created single-payer systems in Medicare and Medicaid, rather than private-public partnerships like Clintoncare and Obamacare. He didn't trust the post-Reagan Democrats when they rose to power, and so he's well placed to take advantage of the failures of their policies.

What makes this battle so important is it's a fight Sanders might be able to win without winning. Even if he doesn't end up beating Clinton in the primary, he is proving that this wing of the Democratic Party is larger than most thought, and he's forcing Clinton, and future Democratic politicians, to take their concerns more seriously than she otherwise would. The talk of socialists and capitalists is really a distraction for this much more specific clash between different kinds of Democrats.