In uniform circular motion, speed can remain constant while velocity changes due to the continuous change in direction. Velocity is a vector quantity, meaning it has both magnitude and direction, which is why it varies in circular motion despite constant speed. The discussion highlights that while the speed of a particle can be constant, the acceleration is non-zero, indicating a change in velocity. Additionally, the concept of helical motion is introduced, where a particle can maintain constant speed while its velocity changes due to the path's curvature. Understanding these principles is essential for grasping the dynamics of circular and helical motion.