agaric an old term for any mushroom, is derived from the classical Greek name for mushroom, agarikon, which in turn comes from the town of Agara, once famous for its mushrooms. The name has survived in both popular and scientific nomenclature, but with meanings which differ somewhat from each other (and, incidentally, from the meaning in classical times).
The scientific classification Agaricales comprises all the families of ‘mushroom-shaped’ fungi, i.e. those which have caps with radiating gills underneath and which grow on stems. All these might therefore be correctly called agarics. But in ordinary speech they are not.