In taxonomy, which is the study of the evolutionary relationships between organisms, there is a distinction made between things that we call monophyletic and paraphyletic. Monophyletic groups are those that share a common ancestor. For example: birds, as far as we can tell, are monophyletic. Structures such as the beak, feathers, etc. that make birds unique among vertebrates (again, as far as we can tell from the fossil record) did not evolve multiple times. There is only one group of birds.
Paraphyletic groups appear to be very similar but are actually groups or organisms that do not share a common ancestor that gives them that similarity (because we presume that every living thing on earth does share a common ancestor somewhere). So to follow the example, birds and bats are paraphyletic. They are the only vertebrates to achieve powered flight but their common ancestor (which goes way back to the proto-reptiles/proto-mammal anapsids) did not have powered flight.
Likewise we have two terms for structures that either are or are not produced by common ancestry: these are analogous and homologous. So my hand is homologous with a bat's wing (because both my hand and a bat's wing came from the feet of those early terrestrial vertebrates) but an insect wing and a bat's wing are analogous (because they do the same thing, allow powered flight, but did not derive from a common ancestor).
OK, still with me? No? Aw, I knew all that science was going to scare folks off. Well for those that are still reading there is a point to my inane ramblings. I have seen a fair amount of lessons based around classification that end with students sorting organisms strictly by morphology (how they look) rather than phylogeny (how they're actually related). So you get wacky groups like "things with wings" and "things that eat other animals" and so forth. This is by no means bad or wrong and is sure as heck the best thing for the real young'ins. But by the time children are in second or third grade they are developmentally capable of going further and are often really interested in stuff like dinosaurs and other animals that no longer exist.
So I encourage those of you who work with young people to strengthen your phylogenetic knowledge and the next time a student asks you if you should group a butterfly with a parrot engage them in conversation about exoskeletons and endoskeletons or segmented bodies or beaks or open and closed circulatory systems. You might think I'm crazy but I've tried similar things and it often works. We should never underestimate how much science a third grader is willing to digest.