OK, to answer my own OP, here's the definitions I used, as a reminder:
Theism: a belief that there is at least one deity.
Agnosticism: not knowing if there's a deity or deities.
Atheism: a belief there are no deities.
If a person says (s)he's an "agnostic", I tend to think that's quite clear. Obviously they mean that (s)he doesn't know if there are any deities or not. To me, that's a logical position, namely if one doesn't know then they don't know.
OHOH, if a person say that (s)he's a "theist", that becomes more iffy because what is their belief based on? In some cases it may be what's called "blind belief", namely that they were just brought up to believe way, and they just accepted it without question. But, there are many who believe that there were some experience(s) that they had that pushed them in the direction of belief or confirmed their belief. With the latter being the case, their belief is logical because at least it's based on something.
But with "atheists" (see above definition), they say that there aren't any deities, but what evidence is that based on? Some atheists poke fun at theists and/or theistic beliefs, which is why I constructed this thread to begin with after seeing that in action here on numerous occasions, including just a few days ago, but I tend to think that the joke is on them. How could they possibly know there aren't any deities anywhere?
Of the three entities, "atheism" is that one that really more of a blind belief, and yet I see some self-proclaimed "atheists" strut around in smug arrogance making fun of theists and what they may believe.
BTW, I've been in all three positions during my adult life, and some here know what I've been through on this, and that's still being reflected in "My Faith Statement" at the bottom of my posts.