The difference is that Saudi Arabia conceded something (many things initially) that the US wanted, namely alliance to counter Iran (
whose democratically elected leader Mossadegh CIA deposed - Operation AJAX - in favor of the reviled Shah who favored US Oil companies but who two decades of CIA sponsored savagery toward his own people inspired the 1979 Islamic revolution.)
From the US point of view SA is the willing bedrock of regional stability,
(other than funding or sponsoring extreme fundamentalist groups, like ahem Al-Qaeda who are dead set on destroying us, and other than sponsoring terrorists group in Iraq, Syria and most recently Yemen, they have been a bedrock of regional stability) even though I'd agree this has become more questionable in recent years.
But look back at the 70s and 80s and you'll understand why there is a relationship there, and why it benefited both the US and the Saud family
(you mean we secure the oil, you peg the price of oil to USD, you buy $Billions of dollars weapons from us, you purchase trillions of US Treasuries, I think I get the gist of the relationship. It's been going on since Eisenhower in the 50's and we are willing to close an eye to the all the naughty things Saudi Barbaria does domestically and abroad. Sometimes we even fight their proxy wars in Syria and Yemen. All in the name of democracy)
You don't want to normalize relations with Russia because Russia has been unwilling to normalize relations on any acceptable terms. Yes Obama and HRC tried, and they also thought Putin was one thing while he later proved to be another.
(Yeah, I mean we just tried to expand NATO at every step, and put an anti-missile shield in Poland, and tried to marshal the Ukraine opposition and install our own guy in there we have done nothing that could be perceived as aggressive towards Russia. We almost went to nuclear war in the 60's during the missile Cuban crisis but that was a different era. Blame it on JFK