Each summer I visit Barcelona, Paris, and London with students, and particularly in Barcelona and Paris, I always gain a deeper appreciation for Art Nouveau. Art Nouveau was a bit of a blind spot in my own education, I now realize. I've included Horta & Guimard in my classes for years, but it's been a pretty superficial treatment. I've treated Sullivan and Gaudí as related but in categories of their own.
In Barcelona/Catalonia, so I've learned, their term for Art Nouveau is Modernisme. This is a direct translation; see the brochures from the St. Pau Hospital below.
A large part of Barcelona, the Eixample district, is full of wonderful buildings in the Modernisme/Art Nouveau style. Indeed, this is what makes Barcelona so satifying to visit: the quality of the 'background' buildings is exceedingly high.
Barcelona's Modernisme is distinctive from the Art Nouveau of Paris or Brussels because it includes more Neo-Classical and Neo-Mudujar influences, as well as the local influence of Gaudi. But it is clearly part of the same movement using new forms of decoration with floral patterns, ironwork and ceramics.
I think Catalonian architects and historians are proud of the term Modernisme, and unhappy that it was usurped by the concept of Modernism. Of course Modernism is quite different from Modernisme.
This also points to the fact that Art Nouveau was a worldwide movement which not only took different forms in different places, but also different names. The UNESCO World Heritage Site nomination for The Works of Antoni Gaudi (1984) makes this point:
"[Art Nouveau was] an authentically creative movement, an international phenomenon distinct from the historicism of the 19th century. It is characterized by the return to natural forms, merged, without prejudice, with the inherited formulas of the past and known by several different names: Art Nouveau, Jugenstil, Liberty, Floreale, Modernism[e], etc."
Here's the Wikipedia page for Modernisme.
And, somewhat obliquely, here's how Sir Nikolaus Pevsner described Gaudí’s relationship to the Art Nouveau:
"Gaudí’s architecture poses even more urgently the problem of how far Art Nouveau as a term with an analyzable, useful meaning can be stretched. That he is first and foremost Gaudí there can be no question."