As far as I know they are all from intel, do the same thing, and yet do not mention each other at all.
So can someone clear some confusion, what and how they are differ
As far as I know. Intel bought appmobi and rebranding it into Intel XDK. Crosswalk is its own webview (runtime) that get embedded in app you build.
Benefits of this are : better, faster cross device compatibility with your app and build in support for features that are not accessible yet in regulat webview (webgl, webrtc, indexedDB..)
The biggest drawback is that you app will be about 10x bigger than normally. And crosswalk required Adnroid 4.x minimum to work.
But now (July 2015) crosswalk have 2 versions, embeded and non-embeded one. Embede is basically what I wrote above, non-embeded will make you app install crosswalk from PlayStore after user install your app. Benefits of that are you wont have to redeploy app if Intel improve its crosswalk.
Hope that makes sense
Appmobi used to make HTML5 cross-platform tools that was acquired by Intel about a year ago and it became the Intel XDK tool.
Intel XDK is a complete HTML5 cross platform development environment, it includes an editor, simulator, device testing solution and cross-platform app build service. Intel XDK supports building apps that uses Cordova APIs and it also supports other unique device APIs (intel.xdk JS bridge APIs)
Crosswalk is a portable runtime for HTML5, Javascript and CSS. Its an open source project from Intel. It is supported in Intel XDK to build Android app using Crosswalk runtime. This runtime has better HTML5 support than the runtime available by default with Android like WebGL and WebRTC... more information here.