President Trump has been feuding, verbally and publicly, with Senate Majority Leader Mitch McConnell. Establishment types like Sean Spicer and Reince Priebus have vacated the White House. This has led to questions about whether a major and durable rift between Trump and the party is coming. Although presidents and their congressional parties frequently experience tension, even during periods of unified government, we have very few examples of presidents who really broke away.

The two comparisons that have surfaced are John Tyler and Andrew Johnson, both of whom governed as presidents without parties. Jonathan Bernstein has written about how these examples illustrate the potential pitfalls of independent presidential leadership and give a sense of what we might expect if Trump goes that route.

But the Tyler and Johnson comparisons are limited. If Trump breaks away from his party, his presidency won’t be like those. It’s likely to be something much worse. Several factors distinguish Trump from these earlier cases, and add up to a clear distinction: Tyler and Johnson were untethered from their parties because of divisions within those parties. They were chosen as running mates for their coalition-building potential, not because they ran against their parties in the first place. And both, unlike Trump, were professional politicians with distinct, if questionable, sensibilities on policy.

Tyler and Johnson were accidental presidents. Trump was elected in his own right.

This is the most obvious difference. No one elected Tyler or Johnson to the top office. When William Henry Harrison died in 1841, it wasn’t even completely obvious what Tyler’s status was. Having a president in office who doesn’t really have electoral legitimacy creates its own problems. But the logic of the situation is evident. In 1840, voters elected a Whig. In 1864, they elected a Republican. When these elected leaders died, people with decidedly different views replaced them.

For Trump, the case is less clear. As much as his primary candidacy was about breaking with Republican Party orthodoxy, his victory in the general election was heavily influenced by party loyalty voting. This makes for a muddled situation. Would Trump lose support among voters who thought they were choosing a conventional Republican? Would congressional leaders lose the support of Trump’s angry base? Maybe both. That would be a pretty devastating situation for a party that controls the presidency and Congress.

Tyler and Johnson were chosen for their unifying potential

By saying that Tyler and Johnson were untethered from party, we lose a lot of the complexity of the party politics of the time. Both were chosen, to some extent, for their unifying potential on the presidential ticket. This is more applicable to Johnson, whose selection across party lines was an explicit attempt to run a national unity ticket during wartime. But Tyler was selected with the hopes of Southern appeal, at a time when the parties were not what political scientists would call ideologically sorted.

The major issues of the day, including slavery before the Civil War, cut across party lines. Tyler’s positions on tariffs put off Congressional Whigs; he favored westward expansion and annexing Texas, which was more clearly associated with Democrats than Whigs (although Democrats were also split on these questions). Johnson was a pro-union Democrat who was unexpectedly tasked with helping to lead Reconstruction.

In other words, their splits with their parties were substantive as well as personal, and happened in a context where serious policy disagreement within parties was not uncommon. They were specifically chosen to represent aspects of their party coalitions — and to make geographic appeals. American political parties are no longer so clearly divided into regional factions, and polling numbers suggest that Trump’s potential for crossover appeal with Democrats is pretty limited. And the party system is more sorted now; party identification is a reliable predictor of issue positions. There’s little room for a rogue president to mix and match policy beliefs on the big questions. This didn’t work out well for Tyler or Johnson, but it would probably be worse for Trump.

Tyler and Johnson were flawed but serious politicians

Each has a few defenders in the scholarly ranks, but mostly they lurk at the bottom of ranking lists and are known for poor leadership. Both had “wild card” streaks that led them into their situations. But Tyler and Johnson were serious politicians with established records and at least some grasp of public policy. Tyler had a long record of service. He embraced ideas that most experts think were counterproductive for the fledging American republic — he was sympathetic to a fairly radical view of states’ rights and held a positive opinion of the Articles of Confederation. But regardless of the content of his views, his disagreements with the Whigs and the Democrats were rooted in ideas about how public policy and government should work.

Andrew Johnson’s personal temperament is often at the center of arguments about his failures. He was reported to be intransigent, lacking intellectual curiosity, and racist even by 19th-century standards. And he was drunk when he was sworn in as vice president in 1865. He vetoed legislation aimed at helping former slaves support their families as they transitioned to freedom. So there’s a lot not to like about Johnson. But some of his deeply flawed decisions came out of legitimately difficult public policy questions, like how to structure governments in the South in the years after the war.

As historian Eric Foner points out, Johnson could have cleaned house in postwar provisional governments. But there were reasons for him to appoint familiar people as provisional governors in the South and to fill patronage slots with Confederates — these choices helped ensure loyalty among the local population, even as they undercut any possibility for serious change or challenge to white supremacy in the South. (Note: this doesn’t really do justice to just how bad Johnson’s leadership was in this period, but the point is that transitional governance poses real challenges.)

Johnson was already untethered from the Democrats, and his choices during the war set off Republicans, leaving him without a clear political identity. In other words, Tyler and Johnson both made some bad decisions in the course of alienating both parties, but they were decisions based on some form of policy logic and attempts to solve real governing problems.

This isn’t so much the case with Trump, either. The barbs exchanged with McConnell about health care weren’t even really about policy substance — the bill McConnell tried to get through the Senate was a lot different from what Trump promised in the campaign. If Trump had taken on McConnell on those grounds, that would be the basis for a substantive policy debate within the party. But he didn’t.

Overall, the evidence has mounted that Trump isn’t particularly interested in the details of governing. His differences with other Republican leaders aren’t primarily about issues or differences of opinion about how to balance competing political considerations. Party loyalty provides some clear line of logic to his actions and some linkage to policy expertise. Without these, we have someone in a very powerful office, in a very volatile world, without these anchors to reality.

It’s tempting, then, to write off Trump’s potential split with the Republican Party as primarily personal. But just as Tyler and Johnson’s party-less presidencies were the products of context and structure — of a mixed-up party system and attempts to balance presidential tickets — Trump’s is also. He was nominated by a conflicted GOP that, despite elite objections to his candidacy, was unable to coordinate on an alternative. Now congressional leaders have been unable to craft a health care bill that basically anyone is happy with — and they seem stalled on other agenda items as well.

It’s unclear who has leverage within the party or what kind of political logic drives its agenda. Emerging divisions between Trump and the rest of the party reflect this — it’s not obvious who stands to gain or what the disagreement is about. And like the party-less presidencies of the past, the situation might be less about individual temperament than about a crisis of governance that extends beyond the party.