Since the "second coming" of the Andalusians to the USA in the late 1960's, horses from Spain and Portugal have been refered to here in the USA as "Andalusians." (The "first coming" was with the second voyage of Christopher Columbus when he brought stallions and mares by the direct orders of Queen Isabella and founded the first stud farm on Hispaniola. This allowed the re-introduction to all of the Americas of horses -- as the earlier horses had died with the ice ages.)
Our Association has used the word Andalusian in all of its advertising, publicity. It is, at long last, being accepted as a known breed. (No more "Appalusian" or "what did you call it??") As the level of knowledge has increased in the USA, there is now a time to make the correct designations for the owners, breeders, and public. A horse which traces its roots exclusively to the Spanish Stud Books is referred to in Spain as Pura Raza Espanola or pure Spanish horse. It is not referred to in Spain as an Andalusian; they believe that gives preference to the province of Andalucia and the breeders there (though that is the historical center of our breed and continues to be the location of the oldest major breeding farms. PRE, or Spanish Horse, has been the designation since 1911 when the Cavalry took control of the Stud Book.
Portugal was not pleased to have the horses which came from basically the same blood lines now (1) left out of the Spanish Stud Book and (2) not even eligible to be called the same horse. They call their horse the Lusitano. One can see how closely related the horses are when studying the Portuguese Stud Book to see that four of the six foundation sires to whom they trace their consanguinity are from Spain.
The name Andalusian has taken hold in most countries who don't have Spanish as their native tongue (Europe, USA, Canada, Australia, New Zealand). Our Association registers pure Andalusians who trace their heritage back in a direct and unbroken line to one or both of these Stud Books. We also have a Half-Andalusian registry where the requirement is that one of the parents be a pure Andalusian (no requirement on the other parent).
One can refer to the Andalusian as a horse from the Iberian Peninsula (which is comprised of Spain and Portugal) -- but why use a third word to confuse the picture? Call it an Andalusian. Or a Spanish Horse. Or a Lusitano. In our association we have some 3,000 pure Andalusians. 88% are pure Spanish; 1% are pure Lusitano; and the balance are a combination of Spanish and Lusitano blood -- still a pure Andalusian! Roughly 80% are shades of grey going towards "white"; 15-17% are shades of bay; the balance are the rare black, palomino, and chestnut. Colors not allowed: pinto, pied. Hope this information is of interest and helps get us all talking about the same horse!!