[NoGravitas]

It's fundamentally a difference about the economy and the value of material change vs. cultural change. The left proper wants liberation for all oppressed groups, including the largest, the working class. Leftists recognize that groups that are more marginalized under capitalism/imperialism (national/ethnic minorities, etc.) will benefit disproportionately, but want a rising tide for everyone (except the bourgeoisie). That is to say, leftists have a commitment to intersectionality and the liberation of those with marginalized identities, but the fundamental, sine-qua-non thing that makes one a leftist is anti-capitalism.

The woke "left" is different; it's largely a phenomenon of the petit bourgeoisie, and is not opposed to capitalism, or oppression more generally; the woke instead want representative members of generally marginalized groups to be proportionally represented in the existing power structures, without any significant change to those power structures. The reason the woke come off as so strident and belligerent is that membership in the professional-managerial class (PMC) is increasingly precarious, and US educational/cultural institutions overproduce people with the qualifications for entry into/maintenance of that class position, relative to the dwindling size of that class.