Zonal statistics as table - inconsistent

[AlisonCook]

I have two feature zone data files, both of which are the same except one covers a wider spatial region (ie. it contains a greater number of zones). When I run the Zonal statistics as table tool using a DEM as the input value raster (same in each case), each feature zone file produces slightly different statistics for the identical zones. Why is this? I'd like to know more about the process Arc uses to calculate the stats - does it use only the cell centroids that fall within each zone, or does it include surrounding cells (which will mean that some cells from neighbouring zones will influence the results)? Any tips are appreciated - thanks!

[AlisonCook]

Thank you for your reply - I found it helpful to understand the process.
One thing I have done is download the USGS tool (NAWQA Area-Characterization) which I found by searching this forum, and used Feature Statistics to Table. It takes a bit longer to process as the input features are processed one at a time, but it gives consistent results each time. It works using the polygon feature class so there was no need to convert the polygon to raster.
Thanks for the advice - I'll try this too.