Pterosaurs and dinosaurs together make up the [Avemetatarsalia](https://en.wikipedia.org/wiki/Avemetatarsalia), which is surprisingly tricky to pronounce. Ave-metatarsal-ia. Which is just Science Latin for *birdyfeets!*
Crocodiles and alligators are not birdyfeets. Birdyfeets plus crocodilians is archosaurs.
This is mostly an accident of how dinosaurs wer first discovered and classified.
Among the earliest dinosaurs discover were f Megalosaurus and Iguanodon. People got a lot wrong when they tried to figure out how these may have looked like in life, but they did notice similarities besides just the size and being dead and extinct for a long time.
So dinosaur was sort of coined as term for creatures like them.
Later more scientifically took these two species and found that they were examples of two different branches of huge group of related animals. They created a definition where the entire family of was dinosaurs. The two branches that these animals were on and all the animals living in them.
Scientifically they just took two animals from either branch and declared that every descendant of their most recent common ancestor was a dinosaur.
This definition cover all the big extinct reptiles walking on land that had all these common features. It also includes modern and extinct birds.
If you want to use the scientific definition and exclude birds you use terms like “non-avian” dinosaur.
A big problem is that alongside the dinosaurs lived other big now extinct reptiles that flew though the air or swam in the ocean. pterosaurs, pleiosaurs and others like that.
Those don’t fall in that particular definition.
Pterosaurs are still closer related to dinosaurs than any living organism (except birds), so we could have easily defined dinosaurs as including them without having to worry about including other living reptiles.
With other creatures that are big and extinct but less closely related this sort of definition would start including all sorts of living reptiles like crocodiles.
Some creatures often marketed as dinosaurs like dimetrodon the one with the sail on its back, they are actually more closely related to us humans than dinosaurs.
So due to the definition of dinosaur being based on how closely related creatures are and the first few dinosaurs we found and recognized and scientifically described, pterosaurs are out and birds are in.
There is no reason why dinosaurs have to be defined the way the were. We have names for groups that include dinosaurs and pterosaurs. Avemetatarsalia is a name that includes dinosaurs and pterosaurs and a bunch of other extinct reptiles. It just isn’t commonly used by non-scientist, but a group that covered the same definition could easily have become the popular name all people knew and the further subdivision be something only scientist care about.
Splits like that are often a debated topic in taxanomic circles. I believe that pterosaurs are considered to have split off from dinosaurs because of a consistent difference in the hip joint though, so that split is based of a noted physical feature found in one lineage but not the other.
But boundaries when one lineage splits from the other can get really fuzzy at times, esp when we’re talking 250 million years ago.
OF note, (and shameless plug) the crew at PBS EONS postcast “Mysteries of deep time” ep 5 (What was the first dinosaur) talks about some of the challenges with questions like this in specific . They also have a youtube channel filled with tons of natural history too
https://www.youtube.com/channel/UCzR-rom72PHN9Zg7RML9EbA
Dinosaur was originally a term for all big lizard-like creatures found in ancient fossils.
Eventually scientists got more information about the fossils and made more scientific categorizations. The term dinosaur was made a scientific term but only applied to some of them. And pterosaurs are not in the group that was named dinosaurs.
This is similar to how koalas are sometimes called koala bears because they resemble bears but they are not actually bears.
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