"A cofactor simply describes the additional chemical component which can be either organic molecules (vitamin) OR inorganic ions (e.g. Ca2+ ions). So a cofactor is like a big branching term to describe the two types: coenzymes and prosthetic groups. So you are correct on that. A coenzyme merely describes a type of cofactor that it is temporarily attached to the apoenzyme part. A prosthetic group describes a cofactor which is permanently bound to the apoenzyme part."