Regarding I actually categorize arts, this is copied from my post on an older thread:
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Archaic military arts:
Kenjutsu
Archery
Historical western swordsmanship
Singlestick
Jujutsu (some ryu and under different names, as the term Jujutsu was not coined until the 1700s and then retroactively applied if memory serves).
Ninjutsu (a case could certainly be made, though I will leave that to a ninjutsu/ninpo practitioner)
Archaic civilian dueling:
Iaido
kendo
historical fencing
Sport fencing
Civilian combat:
Karate (insert ryu)
Hapkido
Keysi
Jeet Kune Do
Wing Chun
Ninjutsu/ninpo (the majority of teachers and students of this art are civilians or are learning in a civilian setting)
Shaolin Kung Fu (yes, those monks were civilians, as are most of those practicing it today)
Daito Ryu Aiki Jujutsu
Tai Chi
And....
...all of the various civilian self defense systems derived from various martial arts and from law enforcement that focus exclusively on surviving a violent encounter and how to handle yourself so that you don't get attacked (too many to even begin naming them).
Fight sport/folk game/martial entertainment/lifestyle-fitness:
Boxing (fight sport)
Capoeira (folk game, fight sport, lifestyle/fitness)
Hadong Gumdo (lifestyle ~ wellness)
Wrestling (fight sport)
WWE Wrestling (martial entertainment)
Kickboxing (fight sport)
Tai Chi (lifestyle-fitness)
Judo (fight sport)
BJJ (fight sport)
Kendo/kumdo (fight sport, lifestyle/wellness)
Taekwondo (fight sport, lifestyle/wellness)
Takkyeon (folk game, fight sport, lifestyle/fitness)
Sport Karate (fight sport)
Fencing (fight sport)
MMA (fight sport)
Aikido (lifestyle-fitness)
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I'm sure that you can come up with other categories and I'm sure that people will disagree with some of my categorizations.
Just to clarify:
Archaic military arts: used in, or in applicable training for, actual use in pre-modern warfare
Archaic civilian dueling: for one on one duels fought prior to the advent of firearms or in lieu of firearms after that point.
Civilian combat: Developed for general purpose fighting outside of a military context. This includes peasants fighting against samurai or knights.
Fight sport/folk game/martial entertainment/lifestyle-fitness: developed and/or adapted from older systems for... well.. fight sport, folk games, martial entertainment, or lifestyle and fitness. Which comprises the vast majority of what you see in martial arts schools in the US. Being in this category does not preclude the art from having SD application.
This is not an exhaustive list by any means, and it is
entirely based upon how I view things (i.e. my opinion

) and is not carved into stone (meaning that I am open to recatigorizing things based on my learning more about the arts on the list).
For example, Capoeira could potentially be slotted into civilian combat, provided that there is a reasonable chance of finding schools that actually teach it as such. I am not familiar enough with what is seen in Capoeira schools to comment on that. Were it not for being very famiiar with the mix of TKD schools, TKD would be strictly under fight sport/folk game/martial entertainment/lifestyle-fitness.
Daniel