When it comes to checkboxes, the standard words used by accessibility tools on Android and other platforms are "checked" and "not checked".
Could you please cite this source specifically?
If these settings look like checkboxes with checkmarks, then these terms are the most appropriate, otherwise "on" / "off" are probably the best. "selected" and "not selected" are used mostly for describing cursor/highlight-based selection of, e. g. files or other multiple items. This is what most screen reader users are accustomed to.
Although I and most users could work with either set of terminology, you have affirmed my point regarding definitions. "Checked" is a description of appearance on screen. "Selected" indicates that an item has been selected or chosen. Regarding the selection of text and other items, yes that is a common use of the word "selected" but the fact that it is common in that context does not preclude its applicability in the other context. We would run out of words quickly if we restricted ourselves to 1-to-1 associations.
If someone says:
"What does that checkbox mean?" the answer would be
"It means you have selected that item.".
A factor in different perceptions is that though my industry experience "selected" has been used in documentation more frequently than "checked". A reason for this is that when drafting documentation the writers may not know if a radio button or a checkbox or some other method of indicating selection will be used, so the more descriptive and widely applicable term "selected" is used.
That all being said IMO there is definitely something to your case especially if there is a source that can be cited regarding "checked" being the default term in Android or other platforms. Also, when dealing with many languages the word "checked" might be a more common word for some users. Then there would be the average of opinions of MiXplorer users, and most importantly what the developer thinks. Last but not least: Even if "selected" seems to be a more widespread standard, a different terminology might carry more weight if it is attached to accessibility services as you mention (hence my curiosity about that source).
As you can see I can logically argue your case nearly as strongly as I can argue my own personal preference, the point being, let's see what the wider world thinks. Thank you for the food for thought about alternate terminology, or as you might call it primary terminology.
