Potting up: usually an act of mercy when a plant is threatening to blow up its pot, making it necessary to move the overgrown plant to a bigger container.
Potting down: moving an over-potted plant to a smaller container, usually done as an emergency procedure. A pot is likely dying by the time you realize its pot is too big and therefore staying wet too long.
Repotting: unpotting, cleaning and repotting a plant in the same pot with fresh soil or substrate. Or moving a plant to a different pot of similar size just because you're sick of the way it looked in the old one.
Adeniums (probably most, if not all, potted plants) have to be refreshed every year or so, even if they do not need to be potted up. How often to do this is entirely up to you. Some people leave their plants alone for long stretches of five years or so. Routine repotting is normally done in the spring, just before the plants go outside when it is warm enough. This is usually the time when you want to inspect your plants and decide whether it has grown sufficiently in the previous season that you can finally raise it to expose the growing caudex underneath.
