what does "martial" really mean and what arts are or are not. Why?

You do realize martial really means military. Anything with sports or sport oriented are not real martial arts/sciences.

The list is very long.

Some are more simplistic and easier for teaching the masses like Shotokan Karate. Others are more complex like Hapkido, Aikido or BJJ or JJJ and some are more advanced in knowledge like Tai Chi, Baqua.

Some have military backgrounds. Some were taught to military long before to public.

Tae Kwon Do was created to teach Korean Army basic combat and fitness and designed to be taught in large groups at same time. So were many of the Karate styles.

Kuk Sul was taught to the ROK Marines in the late 50's and still taught. (also to many US special Forces during Vietnam those based out of Korea). Hapkido has is base also taught to many bodyguards thruout the world. Also taught to the Korean version of Secret Service (also FYI the US Secret Service Presidential Details since Nixon admin). Aikido and Japanese Jujitsu have origins that date back to the Samauri.

Lot of Chinese Kung Fu has various backgrounds and starts some were local and tribal, some were taught to the monks, and some from the royal courts.. Doesn't make it less effective if not direct from military. Most techniques had there origins from actual combat. If those techniques didn't work you would be dead.