Intel has versions of its Core 2 Duo desktop processor aimed at the server market, and has (re)branded the part Xeon 3000. Are there any "real" differences between the Conroe "E" series and the Xeon 3000 series?

Spec-wise: no.

The only difference is intangible. The "Xeon 3xxx" chips are just theoretically higher quality Core 2 Duo's. Theoretically lower heat which equals more life and higher overclock.

Are these chips specifically made to be Xeon's from the beginning or are they just the highest quality batches from the same pile - or just versions created later when their process has matured? Don't know.

The Xeon 3xxx series are simply higher binned Conroe processors. They typically need less voltage to reach a given speed compared to a C2D binned processor and usually generate less heat in the process. It's worth it to spend the extra $10-20 if you want to overclock it like it's going out of style.