Mystara doesn't have deities, and instead has Immortals, so "Nay-Theists" would basically be those that refuse to serve the Immortals, and Flat-Earth Atheists wouldn't exist, instead having the possibility of Flat-Earth Theists, as people that believe that god(s) exist in the setting, even though they definitively do not.
I'm going to dispute this point. I have the rules and lore for Mystara Immortals, including the rules for playing them. I also have the 2e and 3e general rules and lore for deities, and am familiar with specific variants for different worlds.
Mystara's Immortals are deities. Their claims to uniqueness (ie, that they were theoretically all originally mortals, that they get their power through a particular source and method, and that they live in a different place) are absolutely all found in other D&D deities on various worlds. There is
no basis for distinguishing them from D&D deities, other than that for some reason the game designers said so (without providing us any basis or argument for that claim that I'm aware of). We literally have the books telling us all about them, and the claims of TSR that they are different are
demonstrably false, based on the material they themselves have published. I mean sure, someone can choose to be a Flat-Earth Immortalist that asserts that the Immortals are not the same as deities despite all the evidence, based on their faith in the Holy TSR I suppose.
The distinction between deities and other powerful supernatural beings in D&D has varied between the editions. In 1e and 2e for instance, there are demon princes that are actually also deities. In 5e, many warlock patrons are also deities (necessitating the PHB claim that they "are not gods" be interpreted to mean "are not necessarily gods, and do not grant warlock powers by virtue of being gods if they are"). Also in 5e, at least some demons princes (Graz'zt is the given example) have greater power than <a demigod capable of hearing prayers--which is more powerful than the demigod definition given in the DM and implies a form of actual deity based on the history of the game's definitions and usage>. Other editions have made sharper lines between what counts as a god and what doesn't--sometimes coming down to whether or not they can grant spells (which would at least be a clear and definite distinction), but other times being in nature the same as the false claim about Immortals not being deities.
So if you want to make a distinction between powerful otherworldly beings in D&D that are deities versus those that aren't, you're going to have to decide for yourself what that distinction is, since the game has been highly inconsistent about it.
Personally, I keep it straightforward and broadly encompassing. The "Immortal Powers" (terminology inspired by both Mystara and Planescape), the creatures most commonly worshipped as deities, are a specific type of powerful otherworldly beings in company with other specific types of otherworldly such as Archfey, Archfiends, Archomentals, Genie Lords, etc. Following the most common presentation, most of these beings can theoretically grant spells. The Immortal Powers' particular distinction is that their powerful nature primarily derives from alignment with universal principles (the sorts of things embodied by cleric domains--which is why they are more likely to have clerics).
Now a question. Where would Planescape's Athar fit in the terms in the OP? It's possibly the most iconic of D&D's Nay-Theists, but the definitions given actually exclude it from being classed as either a Nay-Theist or a Flat Earth Atheist! They believe that "the Powers" exist, but refuse to acknowledge that they are worthy of being considered deities.
Their definition of what a true deity would be encompasses: 1) Would be morally worthy of worship, 2) Would not be capable of dying, 3) Would not need to derive power from mortals (an interpretation of deities that Planescape leaned into hard). Most of the Athar actually believe such a being (or beings) exists and is the true source of divine power (and there
are Athar clerics who devote themselves to it), but it is "The Great Unknown", beyond mortal understanding or direct interaction.