True dinosaurs fells into the orders Saurischia and Ornithischia (bird-like dinosuars). Other important extinct orders contained the Pterosauria (pterydactyls, etc.), Ichthyosaurs and Sauropterygia (aquatic reptilians), and Placodontia. There are several other less important orders.
All of these orders (living and extinct) belong to the class Reptilia. They are properly referred to as "Reptilians." When you use the term "reptiles" today, most herpetologists (scientists who study reptiles and amphibians) will assume you are talking about the four modern orders.
It is also important to note, as in an earlier post, the bone structure of many of the dinosaur genera suggest warm-bloodedness (i.e. much more bird-like than reptile-like).
The long and the short of it is that both statements are correct - from a point of view.