Despite the jump from one way of wording it to the next, yes. Conversations are Private Messages, just with a different name and a better interface. Instead of having multiple messages separated by Inbox/Sent across many items, all messages/replies sent by each person are all neatly kept in a single conversation.
As stated by the previous poster, you have to "leave" a conversation to remove it from your list. It essentially does the same thing since you won't see it ever again. Other than that, you can 'mark them as read/unread' and 'star/unstar them' (which is most likely the same as marking it as a favorite/important message.