How does job classifications relate to the Equal Pay Act. I am a supervisor in one department making less than another supervisor in another.

The Equal Pay Act applies to jobs where the core duties are identical, and where there is no basis other than persons' respective genders to explain the difference in the pay rates of a male and a female. It doesn't matter what one calls either job.  The fact that you supervise employees in a different department from your comparator of the opposite gender could (but won't necessarily) knock that other person out from being a comparator since the circumstances in which you and the other person are performing your duties may be different.