If you want to label it as just soap and be exempt from FDA rules for cosmetics, then yes, you've got it right.
From Marie Gale --
"...A true soap is one in which “the bulk of the non-volatile portion consists primarily of an alkali salt salt of fatty acids” (according to the FDA regulations). In other words, it is made with lye and oils.
"...The name of the product, net weight and name and address of the manufacturer, distributor or packager are required on the label; the ingredient declaration is not required.
"In order to be exempt from other labeling requirements, the only claims that can be made about a true soap are that it is soap and that it cleanses. A true soap can become a different type of product if other claims are made about it...."