Is there some webpage that tells why some subwoofer fire to the side and some fire down?
Why some Subwoofers are "open" or "closed".
ETC.

Here are some subwoofer design theories overviews you can read up on. Keep in mind that some of the advantages and disadvantages listed here for the different designs are broad generalities and do not always apply to every case.
http://www.danmarx.org/audioinnovation/theories.html

The different woofer firing diections you noted have little to do with how the sub actually sounds, but may have an effect on how easily the sub can be positioned in a particular spot.

Thanks for the link, I think I'll need to read it several times before it can sink in.