The U.S.S.R is a Federal Marxist-Lenonist One Party Socialist State while the Russian Federation (1922-1990. From 1990-1991, it was a Federal Semi-Presidential State... and then there was no U.S.S.R.). The present Russian Federation (legitament successor of the U.S.S.R., though several border countries were member states of the U.S.S.R.) is a Dominant-Party Federal Semi-Presidential Constitutional Republic. The United States has always been a Federal Presidential Constitutional Republic.
All those definitions are confusing but suffice to say that conflicts between the two today are not based on Communist vs. Capitalist ideologies and have not been for close to 30 years. Both countries are today classified as Mixed-Economies (that is there is some balancing between market based economies and planned economies that usually result in regulation that is too nuanced to nuke each other over).
The Cold War wasn't an ideological one beyond the Capitalism vs. Godless Communism playing well in propaganda for government support. The driving force was that the U.S.S.R. was absolutely terrified of the United States' new Nuclear bombs and were really good at intelligence operations, both offensive and defensive. They had a legit fear that the US would nuke them because to date, the U.S. is the only nation to use it's nuclear capabilities in an offensive (Hiroshima and Nagasaki).
Meanwhile, the United States wasn't helping by early hawks actively campaigning to nuke countries (China was the most serious proposal) back when the bombs' radiation effects weren't well known. At the same time, the United States refused to adopt a "Second Strike Policy" out of fear of the superior numbers in the Soviet Ground Army and actively feared the so called Bomber and Missile gaps (this goes to Soviet Intelligence defenses... They knew the US would watch the May-Day military parades and look at all the cool toys, so they took their nuclear bombers... and flew them over the parades in multiple waves, but rather than say this over media, the news reporters would call out names of non-existent bomber divisions, which made the US think Russia had the edge... they never did. The same was true with the Space Race, which the Russians failed to disclose any failures publicly and used rockets that were entirely devised to carry nuclear warheads. The Saturn V of the U.S. Apollo program was the only rocket purposely devised for Space Exploration in the entire space race.).
The 2016 meddling is not the first time in history where Russia has tried to influence the U.S. Elections and they probably tried to do this in every political election in the United States. At present there is little evidence that they affected any real political changes in the current election. It's also known that there are a host of United States led interference operations in other countries that still happen for any number of reason (from stopping popular communist regimes to we just didn't like the popular candidate).
If there is any reason for the current 2016 meddling it seems that the Russians are trying to sow disunion within the United States and not supporting or puppetting any one player. There are theories why Hillary was not supported by Russian propaganda over Sanders and later Trump was that he believed Hillary's State Department was behind protests against his 2011 election and suspicions of ballot issues. In addition, Putin was running to unseat his own party's then-incumbent President (In Russia, you cannot serve more than two consecutive terms as president... but you can serve as many terms as you want... so Two-Terms up, one term down- And a Third Term up is not illegal... in fact, Mendelev was hand picked by Putin to serve the gap term and was Prime Minister in the Legislature for that period.). Putin felt that Mendeleve was a terrible foreign policy leader and Hillary's State Department was dancing mental circles around Mendelev at all avenues. The fact that his latest election was called into question and loudly protested by comparison to other Russian elections steeled Putin against Hillary.