Based on the published specs, these two lenses are essentially the same. The community answer notes that their specifications are identical, so you should not expect a meaningful difference in focal range, aperture, or general optical performance.

If there are any changes in the IS II version, they are likely minor rather than a full redesign—possibly small tweaks to image stabilization behavior (such as panning detection) or lens coatings. There’s no indication here of a significant image-quality upgrade.

So in practical terms: treat them as very similar lenses, and don’t expect a major performance difference from the “II” name alone.