Native Russian speaker, but not a historian here... I'd say that соединенныe is united, as in separate things being as one, while объединенныe is united, as in separate things made into one unified thing. So there's still some separation of the individual things that were соединены, but not necessarily ones that were объединены.

I don't know if you speak any Russian, but if you do, you might be better at it than me so I apologize if this is an insufficient explanation.

Both words have the same root adjective "единённый," from "единый" "united/unified," in turn from "один," "one." The difference between the U.S. and UAE adjectives is the prefixes.

The prefix "с(о)-" most always carries a connotation of "with" or "together." The prefix "об-," to the best of my knowledge, has a connotation of "about" or "around."

So while both "соединённый" and "объединённый" can be translated as "united," there must be a very subtle semantic difference having to do with the prefixes. Perhaps Russians, at the time they learned of these respective states, perceived some nuance in the ways in which both countries were united. The U.S. is a federal republic of constituent states, the UAE (at least partially) an absolute monarchy of constituent emirates. This could lend to different conceptualizations of what "union" was in both nations. The difference might be very hard to translate into English.

I will say, though, I am not a historian, and so I hope this answer does not break any rules, I'm trying to give the best linguistic explanation I can manage. If you'd like a definitive answer, perhaps check out /r/russian or /r/russia. They're both very active communities and could likely provide you with an answer.

EDIT: /u/kaitou42, a native speaker, has been kind enough to give their interpretation in a comment below. Many thanks to them!

I will say that I've seen both used for the United Kingdom, so while there probably is a semantic difference, I'm not sure it's fully agreed upon.

I might suggest /r/asklinguistics ?

I'm not a historian but I am Russian and I can confirm that Соединённые Штаты sounds odd unless you got used to it. However this might have something to do with United Kingdom, which is also called Соединенное Королевство. For me соединенный is also more about one physical object being connected to another. However this might be purely linguistic.

Same thing in Croatian. USA translates to SAD, Sjedinjene Američke Države. The UK, on the other hand, translates to Ujedinjeno Kraljevstvo. UN is also Ujedinjeni Narodi, and same thing with UAE. The difference in usage is more stylistical when not talking about names of various entities. Would like to know what's up in Croatian as well, I can't think of any entity that uses the adjective "sjedinjeno" as opposed to "ujedinjeno" except the USA.