I can hardly believe I’ve never confronted this before, but are the words “ones” and “one’s” interchangeable?
I.e., is there a difference between the phrase “ones dog” and “one’s dog”? I don’t think I’ve ever used the former form before, but when I enter each word into dictionary.com, I get the same page for both.
The words “ones” and “one’s” are not the same. You get the same page at dictionary.com for both (the page for “one”) because they both have the root “one”, the former being the plural of this noun and the latter being its possessive form. “one’s dog” is correct and “ones dog” is incorrect; the right way to use “ones” is something like “I’ve got a twenty in my wallet, two fives, and a few ones” or “He died while surrounded by love ones” or such things.
Thanks for the authoritative reply and explanation for why dictionary.com gives me the same page. My intuition was screaming that “ones dog” was wrong, wrong, wrong, but as I indicated, I’d never tested the proposition before.
Another example of correct use of “ones”: There were blue roses and red roses in the bouquet, but the red ones were prettier. Technically it is the plural of the pronoun “one”.
One’s wrath must be saved for the ones who use apostrophes incorrectly. 
Or even loved ones.
Whoops. I suppose the ones is on me to check for these things before submitting a post…
Sure it is. Say I’m sorting paper money into piles according to denomination; for American dollars, I might end up with a ones pile, a twos pile, a fives pile, and so on. Now if instead of putting the bills in piles I was feeding each denomination to a particular dog, then I would probably refer to them as the ones dog, the twos dog, the fives dog, etc.
I thought long and hard when writing that post about giving some contrived example like this, or even just a disclaimer or clarification as to what exactly I was saying, and in the end let it go. I figured no one would call me on it. I see now what a terrible mistake I’ve made.
My knowledge of grammer is hazy at best, but for a posessive use of an apostrophe, it depends on whether the word is a plural ending in “s” already or a name that ends in an “s” sound where adding the extra “s” would be awkward - in which case use the apostrophe after the first “s”. So, “David’s dog”, but “Jesus’ dog” or “the Jonses’ dog”. Plurals that do not end in “s” get the extra “s”: “chidren’s dogs”.
I would personally write “Jesus’s dog”. After all, I would pronounce it with an extra consonant (as opposed to, say, “the kids’ dog”), so why not spell it that way? [Not that spelling and pronunciation need be so tightly coupled, of course]. But it’s a tricky issue, and for all I know, I’m not entirely consistent (and that’s alright by me).
singular = one | My loved one has a dog.
plural = ones | My many loved ones all have dogs.
singular possessive = one’s | One must watch one’s Ps and Qs.
plural possessive = ones’ | Some of my many loved ones’ dogs did not mind their Ps and Qs.
singular contraction = one’s | One’s doomed to fail with such a dog.
And now for the terrible twos . . .
Well . . . sure . . . and I can also name my kid “Ones Dog” and use it all the time. 