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.