The screw head shown on the left is a standard Phillips head. The
screw head shown on the right is a "Phillips Square Drive", a
combination Phillips/Robertson head, commonly sold under the "Deck Mate" brand, among
others.
Since Home Depot was the major retailer flogging this product, I
initially assumed it was created by the marketing department in order
to allow the retailer to artificially distinguish themselves from the
competition without prodiving real value. However, having now driven
about 300 of them, and used some standard Phillips screws on the same
project, I am surprised and pleased to comment that the combination
Phillips/Robertson drive really does go in with less force and strip
less often. It also stays put on the driver for one-handed
installation - of course this also means it tries to pull the bit out
of the driver when you're done, and with a magnetically held bit
instead of one directly in a chuck, it usually succeeds.