One of the key tenets of NuGet (and an important difference with OpenWrap) is that it doesn't try to change the way you work. Instead, it makes it much easier to do the things that you already do today.
Say for instance that you're trying to use a Foo library, which depends on a Bar library. Today, you'd have to manually find those libraries, copy them to your machine and add references to them. Then later newer versions will come out and you'll go through similar motions to get them updated.
In such scenario, both NuGet and OW will make it easy to bring in those references, but the key difference is that NuGet does it in a way that is completely non-invasive. i.e. it will get the binaries onto your machine and references them in the same way as if you had done it manually. After it has done that, your project file is completely 'normal', without any ties to NuGet at build or runtime.
What this means is that if you get some libraries via NuGet and put your project in source control, another developer is then able to use your project without needing NuGet at all.
The OpenWrap approach has merits as well, but to go that route, you have to be willing to be using OpenWrap all the way, and not easily be able to move away from it.
There are many other differences (like rich VS support in NuGet), but this is what I view as the most fundamental difference between the two.
