Thus, there are various ontologies.
Nothing is implied about objective existence.
Although ontology and metaphysics are often used synonymously these days, in medieval scholastism, esp. To say that would be a category mistake. Please note that my comments are what I take to be the most plausible interpretation of Quine. I am not that directly acquainted with his writings, so I don't offer this as an expert view of what he intended. An ontology is the projection, if you will, of a language system or conceptual framework or way of thinking.