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These terms are vague and some research communities claim/assume that one or the other is enough...

Usually the idea is that global planning sees "the whole picture"/current world state/current assumed world state and local planning only has to work in the close vicinity of the start point.

Some projects leave the handling of dynamic changes in the environment to a "local planner" that can adjust the plan produced by a global planner in an online fashion.

My usual (over-the-top) analogy is:

• Solving Rubik's cube from any given state is a global planning problem.
• Turning a single side might work with a local planner (depends a lot on the setup)