How is "nacho sliced" jalapeño different from regular sliced?

As near as I can determine, "nacho sliced" is simply a marketing term for such pre-sliced, pickled jalapeno peppers. A quick Google for the term brings up several brands which appear identical to one another. There are also similar combinations of the words such as "nacho jalapenos, sliced". The bottle on the right is the only one labelled as such, but they're basically the exact same thing.

So, the only difference? The "no heat" on the right-hand bottle, and some other subtle changes to the packaging. It's marketing fluff, not a real distinction.

Bonus answer: they probably decided that the picture on the right bottle looked healthier, or lighter, or more colorful, or some dang thing.

It might be a case of changing packaging; I've often seen two identical products from the same brand labelled differently, and by a few weeks later one of them has vanished due to a phased release of a new branding. Notice how the pattern on the label is brighter, and the whole label is slightly taller, giving more room for the photo of food on the top. The copyright mark has also changed location slightly.

If you peruse ethnic supermarkets, you'll often find pickled jalapeños that are cut into slabs (cut from stem to tip, often jarred with carrots and onions in the brine, too. It's also possible that the skin might be removed). It's often labeled as 'jalapeños en escabeche'

I suspect that 'nacho sliced' is simply those cut into little circular sections before pickling.

They were two different items (one had heat and one didn't), but they discontinued the no heat one.