Basically it comes down to how the estimate is performed. Classically, the significant wave height is defined and calculated as the mean of the top 1/3 waves in a given record. However, statistical estimates based on time history of the surface are directly available when measuring subsurface wave quantities. Therefore, we use the power spectrum of the surface based on these quantities to arrive at an estimate commonly referred to as H_m0. This is calculated as:
Where M0 is the zero moment (integral) of the power spectrum
Studies comparing the two estimates have shown that Hm0 slightly over estimates the significant wave height by approximately 5%.
So there is a fundamental difference on how the two estimates are calculated, and yes there is a slight difference in the values. Since we use the spectral based solution, we present significant wave height as Hm0 instead of Hs.
More about this can be found in the Principles of Operation manual.