Mugen
Improvisational blade work · acrobatics · street rhythm
Mugen fights through irregular timing, low movement, kicks, spins, acrobatics and whatever angle the situation gives him. The animation deliberately evokes breakdance and other modern movement languages without pretending his style is a historical school with a clean syllabus.
How you can tell
He changes rhythm constantly, attacks from positions a formal swordsman would avoid and treats the environment as part of the technique. His style works because opponents have trouble predicting what 'correct' movement is supposed to come next.
Jin
Formal kenjutsu · economy · school discipline
Jin fights from formal training: controlled distance, efficient cuts, stable posture and a willingness to wait for the decisive opening.
How you can tell
Where Mugen expands a fight into motion, Jin reduces it. The contrast matters more than assigning his animation to one perfectly documented historical school.