The founders of the American Republic knew their Latin.Correctum est, Larry, bene dictum. Nation does not at all mean government or state; there are other words for those concepts. Nation comes from Latin natio, meaning nation, people, birth, or race. Tangentially, the Latin word gens, strongly related to our word gentile, means nation, family, or clan.
That is why they carefully chose the word "federal." In James Madison's original draft of a proposed new Constitution (the "Virginia Plan"), the word "national" was used to describe the proposed new Union. However, this word was explicitly rejected by the Constitutional Convention, specifically because the founders did not see the United States as a "nation" but rather as a "federation." Their vision was for the United States to be a union of sovereign states as opposed to a consolidation of the states into "one nation, indivisible" – and this reality is embedded in the very word "federal."
Latin is thankfully for the most part a "dead language." It is not subject to political mutation and manipulation. It means what it says.
The word "federal" comes into English from the Latin word foedus (genitive: foederis). And in this light, there is no ambiguity whatsoever when it comes to what the founders meant by rejecting the word "nation" and replacing it with the word "federal." When one understands this, all the clever and pompous pronouncements from academicians and government bureaucrats (who want Washington, DC to plan and manage every aspect of our lives) fall by the wayside. For the word "foedus, foederis" [as a noun - r.m.] means: "a league, treaty, charter, compact."
Thus, federal governance is, by very definition, a compact. The Constitution is a compact. The Union is a compact – not a nation. The founders knew their Latin even as most of our modern-day "educators" and bureaucrats do not. Coincidentally, Jefferson Davis's middle name was "Finis," Latin for "end" or "boundary." His generation's passing marked the end of education that emphasized Latin and history and classical ideals, and the beginning of Big Government's brand of "public schools."
Today, very few people are in a position to even know that the Federal government is, by definition, a compact. Most give it no thought at all.
Up until the Tribe and big business took over the West, this was basic, elementary information, learned by everyone who completed sixth grade grammar.
Also, the adjective foedus means ugly, coarse, vile, or disgraceful. That can't be just a coincidink. I think the gods are laughing at us.