American politicians, especially during an election year, often ascribe to Europe all the qualities they most love to hate. They say its governments are dysfunctional, its welfare states are wasteful, its war-weary populations effeminate and, worst of all, its health care systems socialist. But perhaps the most traditional foil to America’s superiority is the Old World’s fixation on class. In places like Europe, the standard story goes, a combination of social snobbery and a stagnant economy limits the prospects of ordinary people. In America, on the other hand, class simply doesn’t exist. Here, anybody can start at the bottom and work their way up to the top.

These days, though, politicians are no longer so confident about the American Dream. Questions about America’s class system—and its strain on the country’s social fabric—have entered the national conversation in a way unlike any time in recent memory. Occupy Wall Street grew popular in good part by contrasting the “99 percent” of Americans who’ve suffered over these lean years to the “1 percent” who seemed to be growing richer even in the midst of a deep recession. This inspired liberals to voice their worries about the widening wealth gap and falling rates of economic mobility more stridently than they’d dared to in decades. As Barack Obama said in a speech in Osawatomie, Kan., rising “inequality gives lie to the promise at the heart of America: that this is the place where you can make it if you try.”

America’s increasingly visible class divisions have been fodder for conservatives as well. Mitt Romney claims to fear that Obama’s “class warfare” is tearing America apart. For all its faults, Charles Murray’s new book Coming Apart takes seriously the decaying state of the white working-class. And Rick Santorum was honest enough to compare the worsening condition of America’s economic have-nots to their counterparts in Europe. As Santorum pointed out, economic “mobility in Europe” is now greater than in the United States.

All this talk can be salutary. It’s high time for Americans to have an open conversation about the reality of their own class divisions. For too long, excessive pride in the notion of a “land of opportunity” has masked the fact that too few tickets to the top are getting punched—and that the lives of those who are left behind are getting tougher. But if some politicians and commentators now go so far as to claim that America’s class system is as rigid as that of Europe, they simply can’t recognize an old-fashioned social hierarchy when they see one. It is true that economic mobility is lower in America than it is in most parts of Europe. But the class system remains much more static and entrenched in, say, Britain than it does in the United States.

If this sounds like a paradox, that’s only because, for most Americans, class is largely a matter of money. If you punch a time clock, you’re working class—even if your ancestors came over on the Mayflower. If your portfolio makes more than you do, you’re upper class—even if you were born into abject poverty. By definition, an American who is born poor but attains vast wealth sheds his original class label along the way.

In Britain, by contrast, class is about a lot more than the size of your bank account. If you live in poverty, you could still be upper class—a member of the landed gentry who has gambled away his estate is no less an aristocrat for being hard up. And if you earn a lot of money, that still doesn’t make you an aristocrat—if you weren’t born into the right family, you may be no more than nouveau riche. Class doesn’t necessitate money, and money certainly can’t buy class.

To understand the difference between America’s and Europe’s class system, we therefore have to make a distinction between economic and social mobility.

Economic mobility in the United States has, according to a host of recent studies, now fallen below European levels. Forty-two percent of American men raised in the bottom fifth of incomes never manage to move up. According to the Organization for Economic Cooperation and Development, how much a dad earns is highly predictive of how much his son will earn: High-income fathers in the United States are able to transmit 47 percent of their above-average earnings to their sons; in Denmark, a father’s high earnings boost a son’s income by no more than 16 percent. America’s educational system favors the rich even more flagrantly: According to another OECD report, a teenager’s performance in science classes is more dependent on his parents’ socioeconomic background in the United States than anywhere else in the developed world.

But the promise of social mobility remains much more real in the United States. In America, it is still possible for a lucky few to transcend their social station over the course of a lifetime. In Europe, even the most successful self-made men forever retain the mark of their lowly birth.

Consider the contrast between Bill Clinton and Margaret Thatcher. Clinton, whose father died in a car accident months before he was born, was initially raised by his grandparents, who operated a grocery store in Hope, Ark. Later he moved to Hot Springs, where his stepfather, a gambler and alcoholic, co-owned a modest car dealership. Thatcher comes from a rather similar background. Born in the distinctly unfashionable town of Grantham, Lincolnshire, England, she was raised above a grocery store owned by her father.

Against the odds, both Clinton and Thatcher rose to become leaders of their respective nations. But whereas Clinton is now unquestionably a member of America’s upper class, Britain’s upper class still regards Thatcher as the “greengrocer’s daughter”—somebody who feebly tried to mask her humble origins by taking elocution lessons. They may have thought she was an excellent prime minister—they may have even voted for her—but that doesn’t mean they think she belongs.

By distinguishing between social and economic mobility, we can remind ourselves what’s great about America—and yet acknowledge that it has a lot to learn from Europe. America’s class system may be less snobby, but there are tangible reasons why Europe has higher levels of economic mobility. From much better public schools in bad neighborhoods to much greater financial support for children born into poverty, most European countries simply do more to ensure that everyone has a real chance to succeed.

American politicians have finally started to acknowledge this point. But most of them still ignore another, equally important lesson. It is that mobility, important though it is in a society that aspires to be meritocratic, should never become the be-all and end-all of economic policy. As John Stuart Mill once pointed out, “if some Nero or Domitian were to require a hundred persons to run a race for their lives, on the condition that the fifty or twenty who came in hindmost should be put to death, it would not be any diminution of the injustice that the strongest or nimblest would […] be certain to escape.”

In other words, if average Americans have come to feel that the game is somehow rigged against them, it may be because it is harder for them to imagine their children winning the desperate race to the top. Another reason, though, is that the prospects for those who aren’t quick enough have gone from bad to worse. What’s truly frightening is not the supposed fact that America’s class system has become the same as Europe’s: It is that, even as a successful few have amassed vast fortunes, so many more have fallen hopelessly behind.