In this particular case, it really doesn’t matter if you scale while in object mode or while in edit mode, but here’s the gist:
When you scale an object in edit mode, you are modifying its true scale. You are literally moving two vertices closer or farther away form each other. E.g. Scaling two vertices {(1, 1, 1), (-1, -1, -1)} in edit mode by a factor of two will yield the vertices {(2, 2, 2), (-2, -2, -2)}.
When you scale an object in object mode, you are applying a scale transformation. The scale transformation is a multiplier for the objects true scale. So instead of taking two vertices and moving them to new coordinates, you are multiplying their positions by a given factor. E.g. Scaling two vertices {(1, 1, 1), (-1, -1, -1)} in object mode by a factor of two will yield 2 × {(1, 1, 1), (-1, -1, -1)} . This will appear the same as scaling in edit mode, but the true scale of the vertices remains the same.
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