The thing about populism is that it never really meant common vs. elite, but refers to the mobilization of particular popular sentiments for political purposes. It's a defining of the ideology of some people as generalizable to "the people." Sometimes this division is along class lines, sometimes racial or ethnic. It's probably too imprecise of a word and needs its constituent tactics broken down because they're applied in some contexts and not in others.
I think nationalism is sometimes an accurate descriptor. It's literally contesting the meaning and boundaries of a nation, either for the purpose of establishing one or laying claim to power within it. That contest is part of democracy and sovereignty, which taken to extremes can result in horror.
As far as internationalism goes, I think you'd be hard pressed to find adherents to the extreme of one world administrative governance just as you'd be hard pressed to find people who want hermit kingdoms. In either case, those who do believe in either can be dismissed as small outliers. Usually what you find instead are proponents of alternate organizations of global political economy as we already exist under a particular form. Sometimes this involves more pluralistic international agenda setting and sometimes it just involves common rules of the road for things like trade, resource control, and enforcement of property rights. Realistically, there is no such thing as a non-global ideology because few societies are non-dependent on the the rest of the world. To subscribe to any political economy is to already put oneself on a planetary stage, even if you prefer to prioritize the local. Sometimes ideologies are called "natural" which is usually just a way of overlooking this fact, particularly considering the variability we've seen across time and geography in human existence. There is very little that isn't artificial or constructed when it comes to any aspect of the social.
So for people who want to prioritize a version of the national instead of the global, we have a lot of terms: nationalist, isolationist, populist, but all of them have negative connotations, mostly due to how they've been used through history. The idea of the nation itself is really only a few hundred years old, which is a really short period in human history, so it's no surprise terms would be unstable. Maybe a better way to think of the difference of ideology you describe is as local conflict over economic and political engagement with the rest of the world over sets of particular issues. The way these sets are grouped are fairly arbitrary, depending on the politics of the day. Claiming that groups who are attracted to one particular set are the most important in the nation we can call populism. Claiming that these sets are universal for the nation and mobilizing to advance these agendas within and as a posture to dealing with others we can call nationalism.
Despite myself, I tend to believe in pluralism, and feel that sometimes certain groups or sets are ascendant in political life until they are displaced by other groups and sets. This is a very American idea shaped by certain historical forces of reconciling liberal democracy with capitalism and migration. I think it's been a useful ideal as America took the lead on setting up a lot of our international institutions post WWII, which is why it's weird that some people try to link it to a kind of anti-Americanism. What seems most prevalent in postwar discourse is the idea that 1) There is hierarchy in the global order and 2) America should be at the top of that hierarchy. This is best described as exceptionalism. Exceptionalism vs. Pluralism is really the contest we see playing out when it comes to how a country relates to the world. All countries have the same internal debate, but owing to US wealth and military might, our claim as exceptional seems easier to justify, which is basically like saying Brock Lesnar should be able to bang most of the UFC roster's partners if he really feels like he needs to.
