Are all dragons the same?
No. "Fantastic Beasts and where to find them" (related to the Harry Potter stories) lists 10 different types of dragons; other fantasy stories also differ among themselves about the properties of dragons.
An organism can only pass on the traits it has. If all the organisms of aspiecesare the same, then they all will pass on the same genes. For example,Dragons all have purple skin. A disease strikes that kills out all the dragons with purple skin. As a result, the spieces would go extinct. However, it there had been some pink dragons, they would have survived and the spieces would live on. Get it?
Smaug's family is never mentioned. In fact dragon origins are rather ambiguous. What is known is that dragons came into the world due to the corruption of the creator's song, by Melkor. His discordant addition brought evil into the world, dragons included. It is not explained whether dragons reproduce, or if all dragons were created at that same time, or if there is some other mechanism to explain how they appear.