Both are private property, yes. And you are correct that twitter legally has as much right to do whatever they want with their product and restrict it however they want as United Airlines does. That's not the point being made here at all and has nothing to do with the discussion at hand.

The parent comment I originally replied to was saying "how can twitter even he a public square if it is a private company, that's a contradiction". And I was just saying that there is nothing preventing a private company from having a product that behaves like a public square, hence that isn't a contradiction or an oxymoron.

Thus stands the difference. Capisce?