In the Constitutional sense of public space, only those aspects of an account that are controlled by government officials would fall under that category. Social media services themselves, at least according to various court rulings, don’t fall under this. They are not “traditional public spaces” and are not taking over functionality traditionally provided by the government. Since the aspects controlled by the government do fall under this criteria both AOC and Trump had to unblock people on Twitter. By blocking they were violating the First Amendment (the first Amendment constrains the government, but not private entities). An account being suspended by Twitter however is not such a violation.
If you are referencing what I think you are, that dichotomy is applied to a specific item of speech in question. For a given statement, if the service provider played a role in authoring or editing the statement, then the service provider is considered one of the speakers of the statement. Thus, the same entity can be considered a publisher/speaker of one statement but not of another.
If The New York Times had a section where people could comment on articles, the NYT would only be considered the speaker on the articles themselves and in comments that were made by NYT employees. The NYT would not be considered the speaker of comments made by others.
As of yet, social media isn’t considered an essential service.