I will say trading plan and trading strategies are the same thing. They are what you do to make successful trades and also to become a successful trader.
Strategy is bigger than plan and in practice of a strategy, you will use different plans to achieve purposes of your trading strategy. They, trading strategy and trading plan, both help traders to aim at gaining success, profit. This is the common purpose of trading strategy and trading plan but it's not correct if you say a strategy is a plan, they are totally different.
Ultimately, a trading plan is essential for achieving long-term success in the financial markets.
It is more about a trading strategy that is broader than a trading plan. A trading plan can help you to get profit in one year, one market cycle but a trading strategy can help you maintain your capital better and gain success in a longer term like 2 market cycles, 10 years or longer.
If you are aiming at long term like this, forget about trading, and switch your focus on investing.
I just have to make research about the difference between trading plan and trading strategy and I saw that you are wrong. Trading strategies are part of trading plan but trading plan is more than just trading strategy.
To know more about the difference between trading plan and trading strategy, you can read this:
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Although trading plan and trading strategy can still be a mattrr if debate,but not in the way you posted about it. That one is not correct.