The guy who created XenForo is the same guy who created vBulletin. He sold vBulletin, and started a company named XenForo a year later (the forum we use now). Part of the sales agreement was that he could not produce a similar product, so when he created XenForo, he renamed "Private Messages" to "Conversations". Same thing, different names, and the story goes on. He was eventually sued by the company who bought vBulletin from him, claiming he used some of the same code from the vBulletin in his new XenForo software. They eventually settled out of court for an undisclosed amount, and the rest is history. But to answer your questions, yes, "Conversions" are what he used to call "PMs" or "Private Messages". They are seen only by the persons listed in the "Conversation".