Product Design Engineer or Mechanical Design Engineer?

I have finished on Budapest Universiy of Technology (Hungary) on Industrial and product design course (the tematics were based on Delft University's). It was a fine mixture of the classic mechanical design and machine design (the analytic side), and the form design and theoretics of design (the art side). So if you are a design engineer, what you design tels what kind of designer are you at the moment.
In my case I wanted to do some art works, but as long as I work, I design only machines and classic mechanic things and I enjoy it. So if you have not decided yet, do not worry just be good in mechanics and art classes too.