According to Meguiar's, their polishes (like the #7 Show Car Glaze) are pure polishes that contain no abrasives. Instead they restore nutients to the paint and restore color and shine to the paint. Wax will just protect the surface of the paint and does not supply any nutrients to the paint. So depending on whose polish you are using, it might be a good step to include. I have found that my paint feels very smooth and supple after using the #7 (not just smooth and hard), so I do think it is putting something back into the paint. While the Meguiar's polishes claim to contain no abrasives, their #9 is a swirl remover/polish. I think they can make this claim because when these products dry they become like a jewlers polishing rouge, and the more they are worked into the paint and dry out, the particles break down into finer and finer particles. That is what levels out the paint and makes it more reflective (shiney). So they don't include any abrasives, per se, but some very mild abrasives result due to the chemical properties of the polish (and you need some abrasiveness in order to level out the surface of the paint and make it shiney).
I think cleaners and clay bars are very similar products, but the clay is better suited (IMHO) to removing defects above the surface of the paint, such as paint overspray and rail dust (rust specs).
Dave M - '97 1.8tm