In everyday talk, Andalusian is a term used as a reference in the States and elsewhere for the spanish, spanish-portuguese and lusitano horses en masse.
However, it is not a reference in such common use in Spain.
In America you have a Registry for Andalusian horses, which includes part breds. We don't have that registry in Spain.
The horse that is listed in the Spanish Stud Book is the PRE - Pura Raza Espaņola - which means Purebred Spanish.
There are set breed requirements (height, appearance etc.) and a horse can only be entered in the Stud Book if his/her parents are both entered.
AS WELL: Every horse who will be used for breeding must pass a Revision at 3 years of age.
There are loads of articles about spanish horses, and how they differ from andalusians here: Spain Horses and FAQs