Martial artists are, typically, all users of armed and unarmed martial arts. For example, Sai uses a halberd to bolster his jumps, while Sabo uses both his martial arts style and stick-fighting. Some characters are able to use multiple arts, like Jinbe (Fishman Karate and Fishman Jujutsu).
There are several martial arts styles that actually focus on weapons, such as the Ramen Kenpo and Kanpo Kenpo. Boxers, in particular, wear boxing gloves as part of their style, and Kelly Funk even equipped himself with spiked gauntlets to augment the damage inflicted.
The combatants shown in the world of One Piece are an important asset to a crew. They are often found in positions of high respect. It should be noted that in the One Piece world, there are two main types of fighting arts: free-form and style-form.
Free-style fighters, who use just their bodies, are considered 'brawlers' or 'street fighters' and not a martial artist. An advantage of free-style is adaptation, free-stylers are not bound by the forms and exercises of style-base fighters.
In comparison, the 'style-based' martial artists in the real world would be practicing the true martial arts. They use traditional stances and attacks that can be identified just like attacks in the real world can identified as Karate or Kendo. Fishman Karate has different stances than the kick-based style that Zeff and Sanji uses.
The known martial artists in Straw Hat Pirates are Sanji, Chopper, Franky, and Jinbe. There exist many martial artists with different fighting styles. In the One Piece world, most martial artists have in their arsenal an inhuman strength and speed (and in some occasion Devil Fruit abilities that enhance their power). Their fighting styles can be martial arts with conduct codes or simply improvised styles with no codes of combat.