Does a catalyst work for both reactants and products?From my understanding, organic catalyst or enzyme does not necessarily work for the product of the reaction because of the shape of the activation site. However I cannot speak for inorganic ones.
Generally, catalysts participate and facilitate a reaction, but the catalyst is returned unchanged. For example, sulfuric acid may be used in a Fischer esterification, palladium in a Heck reaction, pyridine in an acylation reaction, hydroxide in an aldol condensation, cyanide in a benzoin condensation, etc. An enzyme can facilitate a reaction is a similar manner, by being an acid or base catalyst for example. We could say that generally, reactions are reversible. Practically, that is not true as the energy differences of the reactants and products may be so different to prevent the reverse, an explosion for example. If a reaction is reversible, that may not mean the reverse reaction will take place. Le Chatelier's Principle can apply to determine the products.
A catalyst works for either the reactants or the product in a given reaction. If it works for the reactants then the activation site on the enzyme, for example, will only fit on the reactants. If a catalyst is added to a reaction in which it catalyzes the back-reaction, or it aids the products, then the reaction will be reversed. i don't think a catalyst could work for both the reactants and products in one reaction because it wouldn't really be a catalyst anymore; it wouldn't make the rxn progress any faster since it would be canceling out itself by aiding both the reactants and the products. I think this is what you are asking, if not please post more details. I hope I didn't confuse you even more!