I'm studying chess middlegame, specifically about planning. I'm trying to broaden my understanding of the terms - Planning, Strategy, Schematic thinking, and Backward thinking.

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Well planning and strategy are very closely related, one may say that the plan is the execution of the strategy. For eg, in many variations of the closed ruy Lopez, white strategizes to control more space and key points around the black king for a later attack or positional domination and Nb1-d2-f1-g3-f5 is his plan for doing so. Note that black may destroy the f5 outpost by weakening his dark squares by G6.

Another common plan, in fianchetto structures is to play h4-h5, to open lines against the black king or cramp the bishop by playing h6. Here white's strategy is to again grab kingside space and his plan for the same is h4-h5 and maybe h6. Again black may stop this but only by creating a hook on h5 (generally speaking).

I am sadly unaware of schematic thinking but backward thinking or thinking analytically is to see the data in front of you and reason backwards. In chess this can mean that you set your self a goal at the board and visualize that goal and try to reach there from the given position for eg let's say your opponents king is very vulnerable and you know there's gotta be some breakthrough but cant see it by normal calculation. Then you can try to visualize a likely way to mate the black king and having seen this position, work backwards to your actual position and see the set of moves that got you there.

One good book for middle games is understanding chess middlegames by John Nunn

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