Even with the clarification of the intended meaning, the construction of the sentence as a whole has a problem.
Trump might be a populist president, and it just shows to me that Americans are not much a different nation.
As it's written, the portion of the sentence after the comma is acting in contrast to the portion that comes before it.
X might be Y, but Z.
I might be short on cash, but I'll still buy dinner.
What comes after but normally presents something that is surprising, given what's already been said. The word but is the most commonly used conjunction to follow an X might be Y formulation.
In your case, what follows is not contrasting. In fact, it makes sense. When using might be, and is not normally placed in conjunction with it as you've done.
Additionally, you can't compare Americans to other nations because Americans are not nations. You can only compare America to other other nations or Americans to people from other nations.
Last, it's the use of the article that is causing problems. Not much a different doesn't work in the construction that you have.
In short, and addressing those three points, the following rephrasing and restructuring seems to best represent your intended meaning:
America is not much different from other nations, and this is shown to me by Trump being a populist president.
Or, if you want to keep the sentence's original order and use might be, you can also use but and call out the fact that what follows isn't actually unusual:
Trump might be a populist president, but this is not surprising to me since Americans are not much different than people from other nations.
(In both cases, your implied argument is that populism is a criteria for election that's common to most nations.)