Winamp Dashboard is a sort of personalized homepage, that lets you add widgets for news, most played songs, viral videos, Winamp skins.
Winamp Remote is a media server, that allows you to share your music to the world. "Winamp Remote gives users the ability to access their personal collection of music from any internet-connected computer. Support for video and photo sharing and access from internet-capable mobile phones is expected soon. Winamp Remote also contains powerful but easy-to-use tools that let users share listening and viewing experiences with friends." (from the press release)
To use Winamp Remote, you need to install a new application and create an account. Then you can share some of your folders and invite your friends to enjoy your music. They can explore the music library in a browser and stream the songs using their favorite audio player.
Here's the download link you won't find on Winamp site: Winamp 5.3 Full (6.12 MB). Both new features are available in the Media Library.