I would say the functional difference between socialism and communism is though they have similar goals, socialists believe in gradualism and achieving these goals over a length of time; whereas communists want radical change, destruction of the old system followed by completely different systems.
A good comparison can be found in the old Russian Mensheviks and Bolsheviks. The Mensheviks were like the very worst of American squishy, hopelessly p.c. and naive San Francisco liberals.
They passed some of the worst, most childish and stupid laws imaginable, such as the infamous Order #1, which abolished the rank structure in the Russian military, in the middle of World War I. All military decisions were to be made by majority vote. (The most popular of which was “shall we run away?”)
When the Bolsheviks took over, after killing the Mensheviks, they established the brutalitarian regime of Lenin, who at least had the common sense to realize that when every single idea they tried was an unmitigated disaster, to countermand them, and go back to doing something known to work. But when he died, Stalin went back to by-the-book communism, killing countless millions.
And thus the Soviet Union experienced 70 years of failing to recognize patterns of abject failure.
In any event, the subject was Putin and Russia, not China and other communist regimes, who are a completely different kettle of fish.
I consider myself something of a Russian expert, as these things go; but I know some old China hands who are the first to tell you that even after two decades of study, much of what the Chinese do is still inscrutable to them.
Oddly enough, George H.W. Bush, when he was ambassador to China, was one of the few people who so thoroughly understood them that they were terrified of him. Where he picked up this genius is unknown, but he grasped nuances of the Chinese way that most of their own leaders missed.
Throughout the ‘80’s, the assessment was that we were going to be in a knock down drag out naval war with China, for which both sides were in full preparation, but the very idea that somebody like H.W. could exist slammed the brakes on direct aggression on their part.
Since then they have been in the passive aggression mode, and only since weak Barry are they testing the waters to see how belligerent they can be and get away with.
Your studies of socialism/communism their interrelationship is more than merely commendable.
May I suggest a book to help you better understand the Chinese, the Mongols and even the Russians.
Read the History of Gengis Khan by Jack Weatherford.
another book is the Art of War by Sun Tzu.
Both tell you how creative rulers think and conquer established, well established societies.