Put down your pizza, because we have news for you: The Teenage Mutant Ninja Turtles don’t do martial arts! Splinter and the Ninja Turtles are practitioners of ninjutsu, which doesn’t involve any martial arts.
Trainers of ninjutsu were called shinobi, or ninjas as we know them today. Japanese shinobi were primarily specialized in espionage, infiltration, and military tactics (see: cool Japanese ninja movies). Think modern-day spy! Shinobi were selected from the samurai class in feudal Japan, and so most had extensively trained in combat martial arts during their samurai days. This was helpful when they transitioned into the ninjutsu arts and developed non-combative techniques.
The Ninja Turtles don’t have the same samurai experience, but they did pick up those rad weapon skills. Shinobi use select weapons; only as a defense mechanism during their espionage missions.
Donatello’s bo staff and Leonardo’s katana are popular ninja weapons because they’re easily concealed and were accessible for samurais.
The sai, Raphael’s weapon of choice, was commonly used as a farming tool and was not considered to be a traditional Okinawan weapon that shinobi would use.
Michelangelo on the other hand used a nunchaku that was used by samurais for training purposes. Although it wasn’t commonly used during their missions, the nunchaku improved hand movement that could then translate into better use with other weapons.
To answer the question, the Teenage Mutant Ninja Turtles did and did not do martial arts at the same time, and if that confuses you, imagine how Mikey feels!