This came up in an argument with some friends. I know that birds are direct descendants of dinosaurs, shown pretty clearly through the fossil record. However, is it proper to say that birds are dinosaurs, or is there an actual distinction?
I bet you'll be interested about the concept monophyly. Any human-made group of species (or taxon) like birds dinosaurs, primate, bacteria, angiosperm, reptiles, … are either monophyletic, polyphyletic or paraphyletic. This picture explain the concept When the taxon is monophyletic it is called a clade.
Monophyletic taxon are those groups of species that can be considered to be objective in the sense that it represents a group of species where each species in the taxon is more related (in terms of time to common ancestor, not according to their genetic similarity) to any other species within the same taxon than to any other species outside this taxon. This is obviously not the case for paraphyletic or polyphyletic taxon.
Typically, we do not consider a parrot or a deer to be reptiles. Therefore, the ususal understanding of "reptiles" makes this taxon paraphyletic. Now, one should not confound the common understanding (what is a reptile in our everyday life) with the strict definition of the taxon Reptilia, which is a monophyletic taxon (or a clade in other words). Probably the best source for exploring the tree of life is tolweb.org. Here, you will find the clade Reptilia (who include birds, snakes, turtles and lizards). Note: Mammals are within the Reptiliomorpha, not the Reptilia.
It is exactly the same issue with the dinosaurs. When we talk about dinosaurs in our everyday life we do not mean birds. But there is a clade called Dinosauria, which include both dinosaurs and birds.
In short, I would say that a bird is a Dinosauria (monophyletic taxon) but is not a dinosaur (paraphyletic taxon). But this little play on word is not a scientific issue but an issue of english usage.
You will also find in this post an introduction to phylogeny