An asymmetric spec like 600 × 1200 dpi means the device can place or sample detail differently in its two axes.

Typically, one axis is limited by the physical hardware spacing of the print nozzles or sensor elements, while the other axis is created by motion: the paper feed in a printer or the carriage/feed movement in a scanner. That motion can often be controlled in finer increments, including overlapping or “half-step” positioning, so the quoted resolution is higher in that direction.

In effect, the device may have non-square sampling/printing dots (or at least non-equal spacing), so the logical pixels can be rectangular rather than square.

Yes, in principle rotating an image 90° could change how detail is rendered, because the two directions are not identical. In practice, manufacturers also use dithering, multiple ink drops, and interpolation/stepping tricks, so the larger number is not always equivalent to true independent optical detail. Very large figures often reflect these techniques rather than a fully native resolution increase.

So the short version is: one direction is set by hardware pitch, the other by how finely the mechanism can move, which is why the numbers can differ.