The main difference is that the board of directors represent the workers instead of outside shareholders making it democratic
So from the parent comment if “liberals would want a woman CEO, while leftists wouldn’t have a CEO” (paraphrasing) does that mean worker collectives don’t have a CEO or that the CEO is ‘good’ because the board represents the workers (and therefore isn’t leftist)?
Just means the parent comment made a kerfuffle in their verbiage. Leftist aren’t against the job role of “Chief Executive Officer”, or some other such Managing Director. They are against the idea of surplus value being given unnecessarily to a shareholder or owner, as well as unreasonable compensation packages to management, especially at the expense of the general workforce.