In Spain and in other Latin American countries,* the term corporación is not usually used to denote a “corporation” (i.e., an incorporated business entity in the US, generally known as a “public limited company” in the UK). US “corporations” are akin to Spanish sociedades anónimas, and corporación used in this sense should probably be considered an anglicismo.
But, ¡ojo! corporación is indeed used in Spain in at least two instances. Corporaciones de Derecho público are associative entities created by law to defend the economic and professional interests of their members. Examples are cámaras de comercio and colegios profesionales (colegios de abogados, colegios de médicos, colegios de arquitectos, etc.). In other respects, the expression corporaciones locales denotes autonomous entities of local government including ayuntamientos, diputaciones provinciales and cabildos insulares, among others.
*Several Latin American lawyer colleagues confirm that in Mexico, Chile, Colombia, Costa Rica and El Salvador sociedad anónima would also be the closest rendering for a US business “corporation” while, although not a term used often, corporaciones may describe several other types of legal entity.