Karl Marx thought he had discovered a law of history–something akin to gravity. The political system and the cultural environment of any given society were driven by the class system, which in turn was dictated by the ownership of the means of production. Marx (incorrectly) believed that the Europe of the 19th century, the most progressive civilization in history, was dominated by a tiny group of factory owners (the bourgeoisie), who would inevitably be overthrown as the result of the weaknesses of the capitalist system and the vast numerical predominance of the working class. Communism–the rule of the workers, with no more class contradictions–was thus an historical inevitability.
Racial and gender-based woke thought, like Marxism, divides the world into groups of oppressors (straight white men) and the oppressed (everyone else). It does not, however, view this distinction as being based on any kind of law of history, and it does not forecast any kind of happy ending. It focuses on elements of identity that Marx would have considered to be part of the “superstructure,” and thus ultimately irrelevant. It is also based on fact; who can deny that straight white men have largely ruled the world over the past few hundred years?
Wokeness is clearly not a form of Marxism; the two are probably best described as estranged family members. DeSantis uses the term “cultural Marxism” for cynical political reasons; he seeks to discredit ideas that have some basis in American history by tying them to demonstrably false and unpopular ideas that have already been rejected by the vast majority of the electorate.