Hrm! I had taken Providence to relate to Fate in the same way as Cosmos relates to Universe... that is, it's just "what is," but with the sense of purpose or order or meaning or love behind it. So I would also see them as synonyms, but I would tend to "elevate" Fate rather than "lower" Providence, like it seems like you and Butler are saying the Stoics did?

I don't think this understanding is in conflict with Sallustius, who seems to be saying that Providence, in a material context, is called Fate for historical reasons?