You could probably find them on the Internet.
There is Darwinism, Neo-Darwinism, and there are also guys (forgot how they call themselves) who believe that the lack of "missing links" can be explained by instant jumps prom species to species. And i'm sure that is not a full list.
You so don't know what you're talking about. Like at all.
Darwinism = Neo-Darwinism. Every 'Darwinist' since the 1920s has been a neo-Darwinist. Neo-Darwinism is simply the realization that genetics is the mechanism of reproducing heritable variations that evolution requires. No modern 'Darwinist' is
not a neo-Darwinist.
The theory about missing links you're talking about is called 'punctuated equilibria', and is not any sort of splinter group of of 'Darwinism' as you are implying. It is accepted by pretty much everyone in the field. And it does not at all involve instant jumps from species to species, it instead posits that speciation generally occurs when small groups of a species are isolated from the larger population. Mutations pass more easily through smaller populations, and thus these isolated groups will change more quickly than the larger population from which they split off. While their cousins change only very slowly, these smaller populations will speciate 'instantly'- instantly in geological time, which still means tens of thousands of years.
Now, imagine you have a photo of the surface of Mars. But the smallest objects that photo can resolve are a meter across. Anything smaller than that would be effectively invisible. We would say that this photo has one meter resolution. Well, the geological record has about a ten thousand year resolution. Anything that happens more quickly than that is simply extremely unlikely to be recorded. Remember, only those individuals that get fossilized are left in this record, and the vast, VAST majority of creatures that ever lived were not fossilized when they died. So the chances of any individual from one of these small groups getting fossilized during that time is very low.
Go back to the photo of Mars. Imagine you can see a rover moving across the surface. The rover is much larger than one meter. But if the rover moved, but moved less than one meter, you wouldn't be able to tell, because the image can't resolve anything smaller than a meter, remember? So imagine the rover moved two meters. You'd be able to see the move, but to you it would look like it had suddenly jumped a whole meter instantly. Just the same, it looks like one species transforms into another (albeit, very similar) species instantly, but this is only because we only see very few of the individuals who ever lived. It's like a connect-the-dots picture. We don't know everything in between, but we can quite easily see what the picture is. The fossil record holds a clear picture of the chain of descent from species to species. Most of the 'jumps' in the fossil record actually represent no larger a change than, say, the difference between dogs and wolves.