Hands up, I don't actually know much about bone saws. What I do know is that these are both beautiful, hand made antique saws.
The older one is mighty blunt - not sure if that is a requirement for cutting through bone or not.
There is a name stamped on the wooden handle in a way that doesn't really suggest "doctor" to me.
The newer one is marked 'Theatre'. It is very well made. I can't find any reference or info on this tool I'm afraid.