Internal \ public dns name space

No there isn't, it just isn't recommended practice.

The internal name space is usually recommened to be different from the outside (the .com, .net etc..) personally I like seperating them just so you can keep em straight.

Using the same domain names internally and externally is fine - as long as the inside DNS server and outside DNS server never talk to each other. They both also need to think they are the Start Of Authority for the domain.
You would not want to publish your internal addresses to the world from your internal DNS server. You are also much better off resolving internal names internally, instead of going to an external server.
Consider using an additional server for your SMTP gateway that gets the mail, checks for spam and viruses and then sends it to your internal mail server.