Do these sentences have different meanings?
- I never saw such a thing.
- I didn't ever see such a thing.
- I never saw him dancing.
- I didn't ever see him dancing.
- Are both usages correct?
- Is there a difference in meaning?
Ah, Negative Polarity again.
(BTW, I am informed that there is now an NPI tag, which anyone is allowed to use to mark questions with. Feel free.)
Whenever you see a negative (like never) in a sentence, you know you've got trouble. Especially if you see more than one, or if there's a modal in the sentence as well. Luckily, that's not the case here.
First, NPIs. The word ever means at any time, i.e, *anywhen. Except people don't say *anywhen (the asterisk means it's ungrammatical); they say ever instead, the same way they don't say *all two, but rather say both instead.
The interesting thing about the word ever is that it's a Negative Polarity Item (NPI), like any; indeed, it's just a variant of any. NPIs can't occur outside a negative context, which is why it sounds so awful to say
That's why there's a not in
Never is just a contraction of not ever, the same way none is a contraction for not one.
Both of those are fine, because they're negative. One is a contraction of the other, so there's no meaning difference.
As for such a thing, it's an idiom, in this case a pretty frozen one, which indicates surprise at the extreme nature of whatever the "thing" is sposta be. So you get to express surprised indignation at the same time you deny experience of extremes. Pretty useful phrase.
Both usages are correct.
They mean the same thing.
However, the scope of the first is more comprehensive. "I never" implies "in my whole life." "I didn't ever" implies "while I was there at that event we're discussing."
Both are mere implications; unless stated, either scope can be understood.
I think there's a subtle difference in meaning, at least in my dialect: "I didn't ever..." often has more force/emphasis than "I never.." One may say, "I never saw him do that". The emphasis is on "saw" and the implication could be that he may have done it for all I know, but I didn't see it. But if I say, "I didn't ever see him do that", then the emphasis is on "ever", which gives an implication is more along the lines of I don't think it ever happened.