Not a contradiction, but rather compliment each other.
In Shotokan karate we strive for the beauty of one finishing blow technique (Todome), one of the unique aspects of our karate is kime (mental and physical focus), or how to to deliver the total energy of the whole body, in the shortest instant, to intended line of energy at impact.
Shotokan karate is known for powerful technique, at the same time when making strong kime it is easy to lose the smooth transition and fluidity. This is dangerous because if we miss or not finish the fight with one technique, than there will be a qio, space for the opponent to catch us, or at the least, we could miss the chance.
The kata stresses the importance of smooth transition after kime, most of the techniques in kata are from kime to next action, and not from kime into freestyle kamae, and this is because of the danger at the moment of kime, since if I am at good distance for my technique so is my opponent.
Strong kime does not have to contradict smoothness, moreover, properly executed kime should be the best condition and starting point for next technique.
There are 2 most important elements at the moment of kime: 1. Pressure to floor. 2. Total body contraction, in shortest time to line of technique.
Both those elements help us with force production and delivery, transfer of total energy in shortest time, shocking power.
But at the same time, pressure to floor is potential energy, and contraction is potential energy as well, since muscles are like springs.
When we make kime and deliver energy, we are recharging at the same time. The more complete the kime the better the preparation.
Using the breath, we control the pressure to floor and contraction, and using the breath, we can control when to release the energy we store within kime to next action.
The breath is the trigger, the muscles follow the breath.
One idea is to sometimes practice, not thinking of pressure and contraction for kime, but rather, think of pressure and contraction as preparation for next technique.
This kind of training will also reduce excess tension from the kime, and will make both the kime and the preparation/transition, more effective.
One of the reasons for loss of fluidity is too much tension at kime in the wrong places. Yes, contraction is an important element in kime, but it has to be the right contraction, complete, yet without excess, from the inside out, and it has to have elasticity within it, it cannot appear “stiff”. (this is a discussion for another day).
When you can make strong kime and smooth, fluid transition, your kata should be without holes, an on looker should not be able to find space to attack you in the kata.
In Tai Chi Chuan they say that at the limit of softness come hardness, and at the limit of hardness come softness, this is a great way to describe the smooth transition from time to movement and vice versa.