The first seems to be entirely owned by Google. The first only has about 900 icons, but the second seems to have about 2100. Only the second has social network icons like Twitter/Facebook. They are both called Material, so it's confusing.
I'm the Maintainer of Material Design Icons. Just wanted to point out that the project started months before Google open sourced an official icon set (launch was four months before).
The goal is simply to fill in the gap and allow a lot more community involvement/integration. Soon with the open sourcing of Material Design Icons Light alongside the new site hopefully it makes this even easier for other commercial/open source projects.
To answer why there is no social media icons... it's more of a legal thing. We're really careful adding them also emailing the correct sources to verify their inclusion is okay with their brand guidelines, but other times we just add them. Brand icons also can change (Medium has updated their logo like twice since this project launched) which adds more work. We have a pretty dedicated 6 person team so it's not much of an issue anymore to manage everything.
I will say we're going to encourage SVG/vector in the future for web users, but will definitely be maintaining the webfont as it grows.
The first one is the official repository for Material Design icons. As you correctly say, it's owned by Google.
The second one is an attempt to cover the gaps Google left with their set, including much more icons, some of them made by the site's owner/s, some user submitted. They're supposed to comply with Material Design icon's guidelines, but they're not related to Google in any way.
In short: much like stackexchange network, it's a site that relies on user submitted content to make money