Vitamin A is a fat-soluble vitamin, a category that also includes vitamins D, E and K. The vitamin encompasses several chemically related naturally occurring compounds or metabolites, i.e., vitamers, that all contain a β-ionone ring. The primary dietary form is retinol, which may have a fatty acid molecule attached, creating a retinyl ester, when stored in the liver. Retinol  the transport and storage form of vitamin A  is interconvertible with retinal, catalyzed to retinal by retinol dehydrogenases and back to retinol by retinaldehyde reductases.
:retinal + NADPH + H  retinol + NADP
:retinol + NAD  retinal + NADH + H
Retinal, (also known as retinaldehyde) can be irreversibly converted to all-trans-retinoic acid by the action of retinal dehydrogenase
:retinal + NAD + HO → retinoic acid + NADH + H
Retinoic acid diffuses into the cell nucleus where it regulates more than 500 genes by binding directly to gene targets via retinoic acid receptors.
In addition to retinol, retinal and retinoic acid, there are plant-, fungi- or bacteria-sourced carotenoids which can be metabolized to retinol, and are thus vitamin A vitamers.
There are also what are referred to as 2nd, 3rd and 4th generation retinoids which are not considered vitamin A vitamers because they cannot be converted to retinol, retinal or all-trans-retinoic acid. Some are prescription drugs, oral or topical, for various indications. Examples are etretinate, acitretin, adapalene, bexarotene, tazarotene and trifarotene.