In a quick, simplified nutshell it's a system-wide ad blocker that isn't a browser extension. It's different because it's not limited by any web browser or the limitations of its extensions API. It can filter multiple web browsers at once (one ad blocker for all web browsers) and other applications with ads like Steam, uTorrent, etc., it can inject userscripts, etc.
If you're referring to the browser extensions, you can enable the Allow extensions from other stores option in Edge and install the AdGuard Adblocker extension from the Chrome Web Store. The AdGuard Adblocker extension for Chrome will work fine in the new Edge.
Also, yes, AdGuard for Windows will work for the new Edge as well.