Look, this is a website that lists graphic cards and ranks them by performance:
http://www.notebookcheck.net/Mobile-Graphics-Cards-Benchmark-List.844.0.html As you can see, neither the Nvidia GT630 or the Radeon 7640G rank very high, but that's to be expected in your budget (the graphic card is always one of the most expensive components of a laptop). They both seem decent choices.
Naming conventions are a little chaotic but there is a certain method to it. For example, in the case of Nvidia. the first digit is the generation; the second is a reference to its power. 1-2 are very basic cards. 3 has more multimedia power. 4 and 5 can be quite good at gaming. 6 is very powerful, but still reasonably priced. 7-8-9 are usually very expensive and only for the enthusiast.
My card is a 460; as the 4 implies, it's 2 generations older than the 630 you mention. But, if you look for it on that chart, you'll see that it's much higher ranked than the 630, despite being a 2 year old graphic card. So you can get an idea about the performance of a graphic card just by looking at its name. Hope this helps.
EDIT: The computer in your second link is an ultrabook. It's lighter, has better battery life, it's very thin... Those are great qualities, especially if you carry your laptop around with you, but don't matter when it comes to gaming.
