If everything is contained within tubing...inflow water and outflow water and waste...it is a closed-system colonic. A speculum is inserted rectally and the two hoses are attached to it. The Woods Gravity Flow method, the Hydrosan, and Toxygen are some examples of closed-system colonics.
If a thin rectal tube is inserted allowing water inflow...and you expel around the tube into a well and drain that is underneath your butt while lying on a specially constructed table...it is an open-system colonic. The Libbe and Jimmy John are examples of open-system colonics.