From what I have read (which could be incorrect) An HPS bulb requires an igniter to operate and MH bulbs do not. So you can Run a MH conversion bulb on an HPS ballast, but you cannot run an HPS bulb on a MH ballast because it lacks the ignitor for startling the lamp. I hope someone else can clarify.
^That's basically correct. There are HPS conversion bulbs that can work off a MH ballast, but they are hard to find. Also check to see if the ballast is switchable or if it is digital, if either of these then it can handle both MH and HPS.
No, switchable meaning a non-digital ballast designed to handle both MH and HPS by way of a toggle switch. What the switch does is engage or bypass the igniter.