Universities and their non-employees (part two)
In an ordinary conventional company (or more broadly many organizations), everyone present not merely matters to the company but also is paid by the company and actively work for it. They're an employee or a contractor of the company, they get paid for it, and they think of their relationship with the company this way. Even in sectors that are plagued by 'unpaid internships', I think that such people still think of themselves as working for the company, just for free.
This is not how universities work for rather a large number of people present. Obviously it's not how it works for undergraduate students, who are giving the university money in exchange for an education (in theory), but it's also generally not how it works for graduate students either, both in practice and in how people think of it. Graduate students may receive a stipend and work as paid teaching assistants and the like, but even when they do they mostly don't think of themselves as employees of the university in general and working for it. Graduate students are here to get a degree, to the benefit of both themselves and the university, and stipends and the like are tools that the university provides to support them in this. Even paid postdocs are somewhat in this situation, because there is an implicit bargain going on; postdocs are not mere employees working for the university, instead they are being supported while they advance their career with the aid of the university.
(The situation with professors is more complicated and tangled, but there is definitely a strong aspect of give and take because a professor is expected to bring in a certain amount of external funding.)
That members of the university population are this way and feel this way matters for much more than legalities. In a conventional company, the company can impose things on people partly because it can say 'you have to do this because you work for us'. If a university tried to do that, the replies from a lot of its people would likely be rather profane, because the people involved don't consider themselves to be working for the university and so don't concede that the university has that sort of power over them. This is so even if, technically, some of those people are effectively paid part-time or even full-time employees at the time.
I would be remiss if I didn't point out that university tacitly or explicitly encourage this mindset in their members because in practice it's rather to the university's benefit. If graduate students and postdocs viewed the university purely as an employer, they would be basically certain to demand much better pay and working conditions. The university very much doesn't want that to happen (as shown by how universities react to the often quite reasonable requests from graduate student teaching assistants, not infrequently leading to strikes or threats of same).
(The university even encourages this mindset among its paid, full time staff; among other things, this saves the typical university a lot of money in aggregate in staff salaries. Sometimes this causes staffing problems, when the disconnect between university pay rates and market pay rates gets too large to be bridged by 'higher missions' and the like.)
(I've previously written Universities and their non-employees about how universities are in practice indifferent to whether or not many individual members can get their work done, unlike how companies do generally care about this because an idle employee who can't work because of something like a dead computer costs the company money.)