"Never saw" versus "didn't ever see"

Do these sentences have different meanings?

1. I never saw such a thing.

   I didn't ever see such a thing.

2. I never saw him dancing.

   I didn't ever see him dancing.

My questions:

• 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. But 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

• *I have ever been there.

That's why there's a not in

• I have not ever been there.

Never is just a contraction of not ever, the same way none is a contraction for not one.

• I have never been there.

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.
As I said, it's not 100% consistent, but there often is that distinction. You have to rely on context for full clarity.

In everyday speech, most people use "I didn't..." and "I never..." interchangeably. However, there is a subtle difference. The use of "never" can be used to imply that something is no longer possible, or is very unlikely to happen. For example:

• "I didn't see that Broadway musical." - this simply means you did not see the show, and does not imply anything about the future.

• "I never saw that Broadway musical." - this could be used to refer to a show that is no longer playing, so it would no longer be possible to see it.