How are PMOS equations different than NMOS's?
Absolute value is the easiest way to remember, for me.  

The NMOS needs positive voltage between Gate and Source to conduct positive current from drain to source (with drain at higher voltage than source).
The PMOS needs negative voltage between the gate and Source to conduct negative current from drain to source (with drain at a lower voltage than source).  

So, they are just duals of one another.

And the polarities of the current and voltage become very obvious, especially if you draw the FET in place with voltages and currents shown.