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. Currently we are focusing on actions that can be recognized by what they look like as opposed to needing to reason about such unsavory things as intentionality and the like. I just don't know how to do it well enough to be useful. Two other pointers I'd like to include here are two major applications we've constructed during the past two years.