Hi, BMG.
Forgive me for drawing this out, but I felt I had some additional insight to help answer the question.
The classification of organisms used to be categorical, such that animals could be placed into different groups based on whether or not they had a requisite array of defining characteristics. The system works just fine if your intent is just to group things by appearance. However, there is always the question of why you would want to group them that way.
But, modern biology uses evolution as the guide for classifying animals, such that true ancestry and relatedness are more important than morphological features. So, modern taxonomists will group everything that evolves from a reptile as a reptile, and will only distinguish two reptiles from one another by means of subgroups placed within the group "reptiles." Thus, birds would appropriately be considered a subgroup of reptiles, for instance.
This system works well because evolution is considered central to modern biology, and it provides a clearer picture of the history of life, so we are better able to see what factors shape the processes of life. Furthermore, it gives us some predictive ability: we can anticipate some of the ecological traits of some species based on what we know about closely related species, because closely related species are often affected similarly by similar environmental factors.
The problems come in when you start mixing terms from the categorical system with terms from the cladistic system. The word "reptile" is essentially meaningless in terms of evolution-based classification, because it groups things in terms of something other than evolutionary ancestry, and you'll only confuse people by trying to use both classification systems at once.
So, before even bothering to use a term such as "reptile," it's important to understand why you want to use it and what the term is going to convey to the person you're using it for.
-Bluejay (a.k.a. Mantis, Thylacosmilus)
Darwin loves you.