It's pretty hard to say what the terms "progressive" and "moderate" mean in a US context, but I would say that both terms exclude the American far right and populist movements, and are vague as to what they include otherwise. The Overton window has shifted hard to the right in the United States, so it's probably somewhat right of what you may expect from, say, a European perspective. A moderate will probably be sympathetic to limiting immigration, for example, a progressive is likely more in support of immigration. Both groups probably support minority rights (e.g. LGBTQ, Muslim, etc), but moderates less so.
In terms of economics, both terms and parties generally describe liberal capitalist economic policy, which is dogmatically entrenched across the US political spectrum, to the point where most Americans cannot conceptualize economic systems other than liberal capitalism. The main difference in political economic values across the US political spectrum fixate mainly on who pays how much taxes, and subsidies for liberal capitalist businesses. Progressives may be more pro-union, whereas most moderates are generally not.
Moderate and progressive groups can overlap, particularly in a politician who wants to appeal to both, usually by contrasting themselves with the right.
Disclosing my biases: I am an American leftist (or social democrat, if you prefer) living abroad, and I generally have quite a lot of disdain for moderates, particularly in the United States. I'm definitely holding my punches for this comment, though, for what it's worth.
If you have a few minutes of thought to the ~200 countries that 8 billion people are living under, like China, India, Russia, Japan, Iran, Nigeria, Indonesia, Poland, Phillipines, Turkey, and their policies on immigration, LGBT, drug use, freedom of speech/press, you would quickly be disabused of any idea the US democrats are center-right.
What I think is that steeped in a Western European leftist bubble, 95% of the world is right wing to you, and you’re confused on where America stands in that spectrum, forgetting about who’s currently been elected in the rest of Europe like Sweden, UK, Poland, Netherlands, Italy, Hungary, Serbia, etc.
Economically or socially and over what sort of time scale?
As for social policy, it is heading to the right, gaining momentum in the years leading to Trump and making steady gains since. I would characterize the social overton window in the US as the Democrats nailing the left end of the window the wall and Republicans systemically dragging the right end further and further right.
This requires a much longer thesis. In short, war throughout history is quite a centrist position (since it's been waged extensively by both left and rightists). Right now you have the Democrats advocating for defense of a nation against invasion, and a leftist government (Venezuela) advocating for the invasion and annexation of Guyana. When leftist governments aren't advocating for industrial military (USSR), global armed revolution and killing, it's usually said through the privilege and zero-skin-in-the-game safety of being under the US' defensive shield, or it's Pol Pot.
> Democrats is to preserve the status quo in all matters: social
Quite humorous to most global onlookers, I'm sure, as most would not be fond of some Democrats' constant push for "social justice."
> don't forget about Europe when establishing your list of countries to define a global overton window
Europe is 9.3% of the world. Half of which wouldn't agree with you since there are still many right wing governments in Europe and 41% of France voted for Le Pen.
So again, I'd recommend you'd be more accurate in relating the US to whichever country you're in, instead of making statements on the positions of people around the globe in which you seem naive on their governments and history.
The Overton window mainly classifies the kind of ideas that are "politically acceptable" on the stage for which it's defined, using terms ranging from "unthinkable" to "radical" to "popular" to "policy". On the world stage, I would argue that the most left-leaning of European countries define the left end of the window (given that they have enacted left policies), and the most right-leaning countries (e.g. Singapore) define the right end of the window. It's not a matter of proportion.
That said, I agree that the global window is rapidly shifting right, as in your example of France.
Okay, point-by-point:
> Military
I agree that the military does not neatly fit into a spectrum which applies well on the global window of left/right. Reaching instead for political philosophy rather than political practice, I think it's better to introduce the 2-dimensional political compass to understand this rather than relying on the 1-dimensional left/right spectrum: war is more favored by authoritarian politics (which is to say politics that value authority, rather than necessarily repressive regimes, which are totalitarian). I would also say that authoritarianism tends to be more popular on the right, though the Soviet Union offers a clear counter-example. This issue is messy indeed. But, generally speaking, I think that American leftists (as a distinct group from liberals or Democrats) are not in favor of war, whereas everyone right of and including Democrats are generally pro-military and weakly or strongly in favor of American imperialism.
> Social justice
"Social justice" is ill-defined here, and I don't really think Democrats push for it. A positive "social justice", as I understand it, might, for instance, consider reparations, which I don't think any contemporary Democrats have pushed for. Democrats adopt a more equality-oriented (not equity-oriented, which I would argue is more aligned with what "social justice" calls for) approach to social issues, outside of certain matters like ostensible support for affirmative action.
But, I don't think this is the thread to define and argue over whatever "social justice" means. You can send me an email if you want to clear that up.
Is Singapore really among "the most right-leaning countries"?
In 2022, Singapore decriminalised male-male sex. In over 60 countries worldwide it is still a crime, and in over 10 of those it has the death penalty (at least in theory).
While it has been criticised on religious freedom (for banning certain controversial groups such as Jehovah's Witnesses, Hare Krishnas and the Unification Church) – it still is greatly ahead in this area of countries such as Iran or Saudi Arabia. The government is officially neutral between the major religions, and there is no capital punishment for essentially religious offences such as apostasy, blasphemy, or heresy.
Economically, Singapore deviates in a number of ways from right-wing economic orthodoxy – state-owned enterprises play a major role in its economy, close to 80% of its population lives in government-owned public housing, the government runs a universal public health system.
For context, I'm not white, not American, not christian so I guess I have a different pov, but to me Europe was much much more socially to the right than the US. Maybe it's different when you are white in Europe though :)