Oil rig basically just means water pipe meant for doing dabs out of with a nail or enail, usually come with a male joint.
Ash catcher was made to keep "bongs" clean when used for smoking. The are basically miniature bubblers but instead of a mouthpiece the have a male joint to go into a female joint on the water pipe. Just catches ash so the ash doesn't ugly up the main water pipe. You can use an ashcatcher with a jhook (Sherlock type mouthpiece with female joint where the bowl would be) for a bubbler set up.