My idea is that a conversation is more or less between equals; a discussion not necessarily so. If 10 people have a conversation around a table, it evokes the idea of people speaking in turn informally as equals, no "leader" or rank. A discussion around the table, however, could be "chaired" or have a leader or someone such as the "boss". Employees might have a group discussion with the boss but a conversation would be among themselves, such as "around the water cooler".
I believe the distinction lies not in the number of people who take part, but in the tone of the exercise. A conversation is simply oral communication of any sort between people. A discussion, however, is where a subject is considered or examined and argumented, to reach a conclusion.