Well, the thing I'm referring to translates exactly to homeowner association in English. And not only does it do that, the Wikipedia articles link each other.

A tenant's association feels much different. Tenants don't have any decision rights as to what will be done to the apartment block considering they don't own the place. At best they can demand infrastructure improvements from their shared landlords if e.g. the elevator breaks every week.

And a residential association seems to just be a neighborhood association? So just a group of neighbors coming together to organize both political advocacy and barbecues.

This Wikipedia article also mentions the need for an HOA: https://en.wikipedia.org/wiki/Condominium