A solution is not a "path" but the outcome i.e. a filled board. If there exist two options to write in the numbers which both fit the originally provided clues

A solution is not a "path" but the outcome i.e. a filled board. If there exist two options to write in the numbers which both fit the originally provided clues and the Sudoku criteria, then that puzzle has multiple solutions. It's worth noting that "don't guess" technically doesn't change anything at all - a full exhaustive search of all options starting from the top-left corner is a legitimate logical deduction tactic (and a legitimate proof in mathematics), even if suboptimal. If you eliminate all the possibilities of writing in numbers, you're supposed to be left only one way that fits the rules, the unique solution.