Is there ever a time when a "Director's" position is a latteral move from being a "Field Manager"?

Question

My company is cheap in the way of payroll but I think they are off their rocker on this one.

Answer 1

I think you may have just answered your own question. :)  

Answer 2

You need to get your hands on the job description  for each position from your company.  This will tell you if they consider it to be the same position but a different title.  Also consider what you agreed to when you accepted the change.  In my mind if you have increased supervisory responsibilities, this constitutes a promotion and the appropriate salary increase.