Here is Hymore246’s answer from reddit:
Hello, Hymore246 here. Seems your found answer but I will expand on it a bit more. I’ll use a section out of the Martial Arts contributor guide I created to explain the types of styles:
Types of Martial Art Styles
Martial arts in CDDA fall into one of three types: Unarmed, Weapon, and Hybrid.
Unarmed Styles can only be used unarmed or with unarmed weapons. These styles are the most variety in techniques and buffs and will usually give some sort of damage boost, have defense bonuses, or give utility to the player.
Weapon Styles can be used with certain weapons but cannot be used unarmed. Weapons styles do more damage than unarmed styles (due to the weapons) but without the appropriate weapon, the player might as well not have the style. Weapons have much less variety in techniques and buffs and will usually never have damage boosts unless they require setup or the style has a significant downside to compensate.
Hybrid Styles can be used unarmed and with certain weapons. Hybrid styles maintain balance by restricting which techniques and buffs can be used with and without a weapon. Having to choose which way to use a Hybrid is an important part of its balance since neither “side” can do everything at once.
As a rule, if you use a weapon with a style that doesn’t support it, the martial art is disabled for as long as you hold the weapon. The same is true for trying to fight unarmed with a weapon style.
Brawling and Taekwondo are “special.”
Brawling’s gimmick is that you can use the style with ANYTHING. Nothing will disable the style and you always get the benefits of the weapon you use.
Taekwondo is a bit different. The style is never disabled by holding something but you never gain the benefit (damage) of what you are holding. Firearms are usually the best weapons to use with it since you can still melee for decent damage if critters get too close while shooting them.