A big one is just that the US controls both its currency and its monetary policy (meaning taxing and spending). That manes that it can take the steps it feels necessary to deal with loan repayments, such as increased inflation and/or a weaker currency. It doesn't have to convince other countries of it, it runs the currency.
An even bigger one at this point is that the dollar is the world's reserve currency. Things are settled in dollars on the international stage, meaning that the US can't have a current account crisis. It makes the dollars, things are paid for in dollars, so it can make more dollars to pay for things. It is unique in that situation. While it could change, that is how it stands.
In fact, that is part of the reason the US is able to borrow so much, and in some ways needs to. People and nations want to put their money in what they see as a safe reserve, and the dollar is one they seek. To make that possible, the US has to issue debt instruments. They have to be able to buy US dollars.
Yet another difference is that the US has high tax compliance. Most people in the US pay their taxes. There are those that cheat or outright evade, but they are the minority. That, combined with a generally quite low tax burden (compared to most first world nations the US has very low taxes), means that raising taxes in the US is a very valid strategy. People won't be happy, but they'll pay. Greece has real issues with tax avoidance which makes tax increases problematic.
Still another difference is in what the economy produces. Despite what you may have heard on whiny online sites, the US makes a lot of stuff. It is the #2 producer of durable goods after China, and only slightly. It builds lots of things that others in the world want. A good example would be microprocessors. Both Intel and AMD are US companies, and Intel fabs most of their newest CPUs in the US. The chips that run most computers in the world come from the US. Makes the economic situation rather different than a place that relies heavily on tourism.
Finally there's the issue of who owns the debt. Most of the US's debt, about 65%, is owned by the US itself. Of that a large part is intragovernmental holdings, and then debt held by the federal reserve. Of the nations that do hold US foreign debt the two largest, Japan and China, do so for strategic reasons to keep their currency cheap compared to the dollar and thus have a strategic interest in keeping that debt. Greece on the other hand, owes most of its debt to other countries.
It is far to simplistic to look and say "Oh this is all the same!" Public debt is actually a pretty complex issue.