"Classification of pterosaurs has historically been difficult, because there were many gaps in the fossil record. Many new discoveries are now filling in these gaps and giving us a better picture of the evolution of pterosaurs. Traditionally, they are organized into two suborders:
- Rhamphorhynchoidea (Plieninger, 1901): A group of early, basal ("primitive") pterosaurs, many of which had long tails and short metacarpal bones in the wing. They were small, and their fingers were still adapted to climbing. They appeared in the Late Triassic period, and lasted until the late Jurassic. Rhamphorhynchoidea is a paraphyletic group (since the pterodactyloids evolved directly from them and not from a common ancestor), so with the increasing use of cladistics it has fallen out of favor in most technical literature.
- Pterodactyloidea (Plieninger, 1901): The more derived ("advanced") pterosaurs, with short tails and long wing metacarpals. They appeared in the middle Jurassic period, and lasted until the Cretaceous-Tertiary extinction event wiped them out at the end of the Cretaceous."
Pterodactyls evolved directly from Rhamphorhynchoidea. So of course, Rhamphorhynchoidea began to phase out (disappear) as they gave rise to pterodactyls.
That is the pattern.
The Rhamphorhynchoidea appeared in the Late Triassic period, and lasted until the late Jurassic. Pterodactyls appeared in the middle Jurassic period, and lasted until the late Cretaceous. This makes perfect sense - an overlap period - a transition.
Moving to the disappearance of pterodactyls and the appearance of modern birds we see the exact same pattern. "The gradual decline of pterosaurs at the same time modern birds radiate."
Pterodactyls began to disappear (phase out) in the late Cretaceous as they gave rise to modern birds which began to appear at that time, with an overlap period.
The Cretaceous-Tertiary extinction event DID NOT WIPE OUT THE PTERODACTYLS at the end of the Cretaceous. The pterodactyls phased out as they gave rise to modern birds.