To be able to move through a full range of motion at a joint is to be flexible. Being able to move that same joint through various motions and directions is to be mobile. Firing the right muscle fibers, at the right time, in the right sequence, across multiple joints is coordination, or movement skill. A skilled martial artist can generate a significant amount of power in a punch or kick. A skilled weightlifter can move a significant amount of load. Ask a martial artist who does not lift weights to perform a heavy-loaded squat, or a weightlifter who does not practice martial arts to make a powerful kick, and the results will be less than impressive.
Strength and power are not just about the ability to produce force. The person producing force must first move well. Adding force production onto movement skill is strength and power. Adding force production efforts onto poor coordination (you can move or you can move it, but it doesn’t look pretty) will enhance poor form, decrease long-term force production, increase chance for future injury, and create compensatory responses in other areas to utilize muscles and tissue that assist (when they aren’t supposed to do so).
Slow down, reduce the load, and reduce the current range of motion whenever poor movement skill is present. Continue to move slower, with light or no loads, until it is fluid and smooth. It’s a simple recipe that few people follow, so most people get injured or sidetracked frequently, or simply never attain higher movement skill and optimal force production. Train movement skill, and overall force production will be tremendously improved.