Actually... the conversion left by Ospho if done correctly should be zinc or iron phosphate. If you keep the metal wet long enough it etches the good metal while dissolving the rust. The phosphate coating left behind should be of matte, grey, uniform appearance and is an excellent surface on which to paint.
Ospho and similar phosphoric acid washes aren't normally called conversion coatings. Yes, they dissolves rust and leaves a phosphate converted surface on the metal. However, what people generally mean today by a conversion coating are chemicals that act on the rust, partially convert it to a phosphate, and then cover it with a primer-like material... all in one step. Duro Extend comes to mind when thinking about hardware store stuff. Eastwood's Rust Encapsulator comes to mind when thinking about a more high-end converter/primer.
It's always better to remove as much of the rust as possible before applying any coating. The phosphoric acid washes are a good way to do that.