I having hard time to understand the differences between action and motion planning. Does motion planning only involve finding trajectories for mobile agents?
Action Planning is used to formulate strategies to achieve a certain goal. The output of this stage is a list of actions, when executed in order, will lead to the desired goal. See Goal-Oriented-Action-Planning for more info.
Motion planning, just deals with one particular aspect of planning: movement. This particular problem is typically solved with a Path Finding algorithm, for which the most commonly used solution is called A*.
In my A.I. implementations, the path finding towards a specific place/object is typically a single step in the Action Plan, which I generate using G.O.A.P.