Compare the following two images:
The path planning is somewhat trivial. There's only one path: the rope. The motion planning on the other hand is not that easy.
In a maze the path planning is hard and motion planning is easy:
Of course both planning tasks can be easy or hard at the same time or anything in between.
They are linked to one another in that
- the planned motion should follow the path or follow that path closely
- the current motion can influence the path planning. If driving in one direction at a high speed, a sudden change in velocity might not be the best idea even if that would be necessary to get on the shortest path. Or the starting pose of a nonholonomic robot, which influences the possible path significantly.
They are separate in that
- motion is related to time (change of position over time), but the path itself is not. Even if the motion goes along the path exactly it could have various trajectories for velocity and/or acceleration. Your robot could stop for example to let another robot cross its path, which is a change in motion but not the path itself.
- motion can be influenced by other things, like wind for example
Neither list is exhaustive.
Which the terms is better than ? motion planning or path planning ?
There's no "better" term. It depends on what you are describing.
For anything that involves moving a physical robot, I'd use motion planning.
How do I get this thing from here to there? could be a question you are answering.
If the robot itself is abstracted away and you are only planning a path of a point through a maze I'd use path planning. What's the shortest path from point A to B? could be an example question.
But again, both planning tasks are connected. If you ask What's the shortest possible path? then certainly the geometry and motion capabilities of the robot determine what's possible. You do both motion and path planning at the same time. Using either term should be fine here.
This holds true for the other cases as well. Both terms can be used interchangeably because the definition of motion and path aren't very clear. (a path implies that a motion happens along it and a motion necessarily happens along a path). You are usually doing both to some degree anyway.