There are steps you're meant to go through before and during each move. We were taught "CRAP": you Communicate your move, the opponent Retreats, you Advance / Attack into the now empty space, the opponent Parries "into" the attack, but their body is out of the way. The idea being here that if you forget the choreography at any point, you're still safe, because you can't attack anything before the receiver has retreated out of the place you're attacking. However, the trick is to do this as smoothly and fluidly as possible, because that sells. It takes practice and maintenance not to let the emotion and adrenaline of the scene take over, and stick to the process, while ignoring the muscle memory of the choreo. It's often not considered an important skill during an audition by casting directors or directors, relative to credits and actual acting, and therefore not by actors themselves. Result: dangerous fights.
But cardboard or foam swords? No way. You want the audience to be on the edge of their seats, and that requires metal.