Backtracking builds a solution one choice at a time and abandons a path the moment it cannot possibly work. It explores a tree of partial choices, going deeper while things look valid and retreating when they do not.
Plain brute force is blunter. It generates every full candidate, then checks each one at the end. It never notices a doomed path early, so it wastes effort completing arrangements that were broken from the start.
The difference is when you check. Backtracking tests constraints during construction and prunes dead branches before finishing them. Brute force tests only after building a whole candidate.
That early pruning is the whole payoff. On problems like placing queens or filling a grid, backtracking skips huge regions of hopeless combinations, while brute force grinds through all of them.
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