I would say that the terms "sand blasting", "grit blasting" or "shot blasting" all imply a similar process. That being a process intended to remove something (paint, corrosion, etc) from the surface of a component, usually a metal component. The term "shot peening" would imply a much more energetic and controlled process where metal/ceramic shot is directed at high velocity onto a metal surface to put the surface layer into compression.
I think the best terms to use for describing a process to clean a surface are either "media blast" or "grit blast", since there are numerous types of abrasive media used such as sand, glass beads, baking soda, walnut shells, ceramic particles, metal slag, or even frozen CO2 powder.