So Reddit's a publisher (because most of the subreddits have various on-topic rules for posting) and my newspaper's a platform (because their rules for posting comments are what's prohibited).
One of the problems with trying to use an actor's own policy to distinguish between platforms and publishers is that the goal of creating such a distinction in the first place is to restrict the ability of the actor to undertake certain policies.
I don't know of a perfect formal definition, but this kind of gives a rule of thumb: is the content considered their own voice? For example, The New York Times is a publisher, because if an article on their website says X, then saying "The New York Times says X" would be reasonable, but Facebook is a platform, because saying "Facebook says X" just because a post on their website says X would not be reasonable.
Whether you say "The New York Times says X" or "Astead Herndon said this" is entirely subjective, and has more to do with what culture currents you pay attention to than with anything particular about the NYT. Illuminating counterexample: a pretty good chunk of nerd Twitter routinely refers to "what HN has said".
A billboard is a publisher; the content there is clearly governed.
So the criteria seems simple:
* is content freely posted? What is the approval process for content?
* if content is freely posted, are the rules for removing content uniformly applied and viewpoint neutral?
* what mechanisms exist for appeal, protest, modifying the rules, etc?
Platforms are defined by what they don't allow.
Publishers are defined by what they do allow.