Point density grid units?

I have a SfM tie-point cloud, but lets pretend it is a lidar cloud.  I would like to make a raster where the value of each cell is the number of points per m^2. That value will be influenced (i.e., more or less smoothed) by choices about how big an area I am averaging over and what window I choose, but it should not depend on the final cell size.

When I load the point cloud and select "color lidar by point density", the numbers look correct, meaning that the colors on the map and the corresponding values on the colorbar look about right. But when I do Analysis/Create density grid from point data... and select Area Units -> Square Meters, the numbers I get are different. They should not depend on the other parameters (Search Radius, Cells Per Radius, Density Type), should they? I was using Population Field <Point Count>, but I also tried Density. I get different numbers, depending settings. What am I missing?

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