What the shape decides

What A⁺ gives you depends entirely on the shape:

• More rows than columns (tall — too many equations, usually no exact solution) → x = A⁺b gives the x that makes Ax as close as possible to b. This is least squares.
• More columns than rows (wide — too few equations, infinitely many solutions) → x = A⁺b gives the valid solution with the smallest norm.

Same function, two completely different jobs, chosen by the geometry rather than by an argument you pass.