I thought the difference between Trotsky and Stalin, in essence, centred on the fact that Stalin denounced the international project of converting the whole planet to communism, and punted for communism at home, and Trotsky didn't. Lotsa bits and pieces may have adhered to both pov's since those early days and interpreted and reinterpreted by 'followers'.

I thought that cultural Marxism came to fame with Frankfurt School:

https://en.wikipedia.org/wiki/Frankfurt_School

Haven't the time to delve into it. Just my tuppence.