If anyone else is wondering what the point of "square samples" is, I did some research and found (apparently) an explanation by the person who implemented the feature:
https://blenderartists.org/forum/showthread.php?342753-Square-Samples&p=2684769&viewfull=1#post2684769
Just in case the post should disappear:
"It's a feature I added. Basically brings Cycles more in line with Arnold. Noise in a path tracer takes longer to clear the longer a render goes on, which maps fairly closely to a n^2 curve. So basically, using squared samples allows every increase of 1 to equal a meaningful amount of noise reduction, and it allows an artist to have a very simple table of values stored in their head to clear noise for various common scene types." - m9105826 @ Blender Artists forum
