The simple answer is both.
Technical mastery is absolutely necessary for the expression of speed. In the most simple exercises, it is important to be able to relax the antagonists and superfluous muscles in order to facilitate reciprocal inhibition. But similarly, the speed of more complex movements depends on optimal coordination of position, centre of balance, centre of mass, timing of contractions, and other factors. The stride rate of a runner, for example, is dependent on the position of the lower leg during the swing phase, since lower leg mass controls the moment of inertia.
However, speed is also governed by the contractile speed of muscle, which depends on fibre type, length, orientation, and thickness, as well as neural development and innervation of motor units. Type II "fast twitch" fibres produce more force than Type I "slow twitch" fibres, and that force is produced more rapidly. (Both factors contribute to the speed of joint movement.) Longer muscles contract more rapidly, since the contraction of sarcomeres traversing the muscle fibres are simultaneous, resulting in a greater absolute distance of contraction in a given amount of time. Speed of contraction is linearly associated with the angle of orientation to the attachment, but force production is a function of the sine of that angle, creating a complex relationship dependent on joint position. Similarly, force production, acceleration, and hence speed, is proportionate to the cross-sectional area of the muscle. And the development of larger, more explosive (Type II) motor units permits far greater and more rapid force production.
This simple analysis might suggest that the qualities of the muscle, nervous system, and physical geometry play a greater part in speed development—and that is probably true—but the role of practice and technical mastery should not be dismissed.
I hope that makes sense.