A "plan" is a description of what is to be done.
"Planning" is the act of devising a plan.
A "strategy" is much more than that. Whereas a plan is deterministic, a strategy is thought through more deeply and takes account many possibile events, which may be unknowable, and plots a course of action that is adaptive, thoughtful, and reacts as needed. For example, a military commander needs to have a strategy, not just a plan.