Bathrobe sent me this Stack Exchange thread set off by the simple but excellent question about Russian: Why are United Nations and United Arab Emirates translated as Объединённые, but United States as Соединённые? The first answer is by Nikolay Ershov:
Соединённые is historical, used AFAIK only with the US and the UK (Соединённое Королевство, which loses overwhelmingly to Великобритания in frequency of usage. The English term “United Kingdom” dates back to 1707.) As a translation of “united”, it would sound “off” nowadays because the word in its current usage properly means “connected”, which isn’t quite the same thing.
The second is by Quassnoi:
Объединять and its derivatives were not used in Russian before about 1850.
Kostomarov did use it time to time in his works, however, he mostly used соединить wherever a modern Russian speaker would have used объединить:
Итак, вместо того чтобы идти соединенными силами на половцев, Владимиру приходилось идти войною на своих.
Рязанские и муромские князья уже прежде были с Андреем заодно, соединенные войною против болгар
So yes, объединять is just a more modern word.
My own response, before he found that thread, was “I’m pretty sure соединить implies a closer union, a melding into one thing, whereas объединить is more ‘joining forces,’ and thus more appropriate for the UN (which, unlike the US, is not a consolidated polity, just a group effort).” I’m curious what my readership has to say about it.
Bathrobe wanted the information for his own post Mongolian-Language Names for International Organisations as used in China; if the topic sounds at all interesting to you, I highly recommend it — it’s very thorough (and has lots of Russian).