Are brazed drills and electroplated drills the same thing?

Yes, and no.

All brazed drills are electroplated, but not all electroplated drills are brazed.

Brazing is a type of electroplating that bonds the nickel more consistently to the metal surface and creates a long lasting, more stable bond on the drill. The diamonds will hold longer and the plating will hold up better to continuous use than a typical electroplated tool.