In May, the Fetch as Google was updated. There are no details on the update other than adding the render feature. Prior to that, it was an older version of the googlebot moved outside of the queuing process. The differences were slight. It is good when you want a page indexed right away but not something I recommend unless it is important to update Google's index for expediency.
Historically, if you fetch a page using Fetch as Google, you would see that Googlebot will come along again in just a few days. This is because the Fetch as Google is intended to be just temporary and did not tie into the index the same way that the normal Googlebot did. It may do so now. I suspect the popularity of the tool had something to do with the update. There are advantages to this option such as getting your page into the index fast. Previously, the page will not fully perform as it normally would. The reason was that a certain amount of trust was given and the page could perform higher than normal- a pseudo boost in obvious search terms where as the page would actually perform differently overall if naturally discovered.
Some try and game Google with Fetch as Google. I do not suggest over using the tool for this reason. There are, however, times when getting a page in the index fast is a must. Then this option is perfect. Use it sparingly. But use it when it is important. Otherwise, I would just wait till the standard Googlebot comes along.