How to Calculate Mosfet Voltages
B is body on a MOSFET, not base.  The relation you posted is true regardless of model - it's how the pin voltages are defined.  

The voltages of the source, drain, gate, and body pins are Vs, Vd, Vg, and Vb.  However, the absolute voltages are not important - the differences are.  So the differences are defined as Vgs = Vg - Vs, Vds = Vd - Vs, Vgb = Vg - Vb, etc.  

Following this convention, Vdb = Vd - Vb and Vbs = Vb - Vs so Vds = Vd - Vb + Vb - Vs = Vd - Vs.