Let us discuss cofactors and coenzymes in the context of vitamins. A cofactor is non-protein chemical compound bound to an enzyme to assist in catalysis. Here is some good MCAT vocabulary. An enzyme without a cofactor is referred to as an apoenzyme, and the completely active enzyme (in addition to the cofactor) is called a holoenzyme. (This level of terminology often appears in an MCAT passage, but you can almost always decode the meaning from the context). For example, vitamin K is a cofactor for proteases involved in blood clotting. A carboxylation reaction which depends on vitamin K converts glutamate side chains of prothrombin into γ-carboxyglutamate, which is a strong chelator of Ca2+. This allows the calcium to serve as a coordinating bridge, a mordant, to anchor the prothrombin to phospholipid membranes in proximity to the clotting factors that activate the zymogen.
Coenzymes are non-protein molecules that carry chemical groups between enzymes. Some coenzymes are vitamins. For example, folic acid, a water soluble B vitamin, acts as a porter in the cell of various carbon groups, methyl, formyl or methylene.