Subtle differences. Audax is where a group of riders get together and ride together for the entire event. Usually there is a leader, and he sets pace, issues instructions, keeps everyone organised. Probably little different to pelotons, except there is no surging, breakaways or somesuch. Someone drops of the back, and the group slows to bring them back on. Everyone stops to sleep and eat at the same time. With true Audax style, the average speed is expected to be 22km/h. It is not that popular in the US, but quite popular in England and some parts of Europe.

Randonneuring is simply long distance organised rides at the individuals' own pace. You can ride together, draft together, you can jump into other beds all day and night... or you can ride alone. Just so long as you come in under the maximum time allowed. The Audax philsophy can be layered over the randonneur one (ie, Audaxers ride in randonnees), but the reverse does not apply.

If you get my drift.