Movements are typically atomic, with no distinct parts. To recognize movements one only needs a description of the appearance of the motion. Time can typically be handled by only linear scaling. Sitting down or swinging a bat are good examples. Activity is a sequence of either movements or of static configurations.
Time is manipulated by some form of dynamic warping.
The gesture literature exploiting HMMs is a good example. Still only the object or objects in motion needs to be considered, not the surrounding context. Action are the high-level entities that people typically use to describe what is happening. Representing and recognizing actions requires qualitative descriptions of time, such as intervals. Context becomes fundamental, though how much one has to reason about context is unclear.