Explanation:

Enzymes are biological catalysts that speed up chemical reactions in living organisms. They are usually made up of proteins and sometimes require additional non-protein molecules called prosthetic groups to function properly. Prosthetic groups are small molecules that are covalently attached to enzymes and are necessary for their activity.

Coenzymes:
Coenzymes are a type of prosthetic group that are organic molecules and often derived from vitamins. They are loosely bound to the enzyme and participate in the catalytic reaction by transferring chemical groups between different molecules. Coenzymes often act as carriers of specific functional groups, such as electrons or chemical moieties, and can be recycled and reused by the enzyme.

Cofactors:
Cofactors are another type of prosthetic group that are inorganic or organic molecules. Unlike coenzymes, cofactors are tightly bound to the enzyme and are essential for its catalytic activity. They can be metal ions, such as magnesium, zinc, or iron, or small organic molecules known as coenzyme precursors. Cofactors help in stabilizing the structure of the enzyme and facilitating the catalytic reaction.

Messengers:
Messengers, as mentioned in the question, are not involved in the attachment to the enzyme or the catalytic reaction. Messengers are signaling molecules that transmit information between cells or within cells, such as hormones or neurotransmitters.

Inhibitors:
Inhibitors are molecules that bind to enzymes and decrease their activity. They can be either reversible or irreversible inhibitors. Reversible inhibitors can bind and unbind from the enzyme, while irreversible inhibitors form covalent bonds and permanently deactivate the enzyme.

In conclusion, the prosthetic groups that get attached to the enzyme at the time of the reaction are called coenzymes. Coenzymes are organic molecules derived from vitamins and act as carriers of specific functional groups to facilitate the catalytic reaction. Cofactors, on the other hand, are inorganic or organic molecules that are tightly bound to the enzyme and are essential for its activity.