Is .NET Execution Environment (DNX) similar to Mono?
Yes, DNX compares pretty well to Mono's mono.exe. Or for that matter the runtime of other VM languages like Java (java.exe) or Python (python.exe). They all solve the same chicken-and-egg problem, they run on operating systems that don't know beans about the VM. It has to be initialized first, the program's entry point needs to be located and the Main() method needs to be jitted before your program can start running.
One small difference in DNX with these other VMs is that it keeps the CLR and the jitter still in a separate library, coreclr.dll. The other ones are monolithic with all the runtime support code compiled into a single exe. Keeping it monolithic improves cold-start performance. Probably something that will happen with dnx as well, once CoreCLR stabilizes and doesn't have umpteen different beta releases.
This otherwise follows the architecture of .NET on Windows, it is c:\windows\system32\mscoree.dll that bootstraps the CLR. And the CLR and jitter are separate DLLs, clr.dll and clrjit.dll for .NET 4.x. Mscoree uses significant trickery and deceit to make it look like you can start a managed program from a single EXE file. Particularly the trick to create a 64-bit process from a 32-bit EXE file is heroic, it patches internal operating system loader structures to accomplish that feat. This requires Windows itself to be aware that an EXE contains managed code. Trickery that does not translate well to other operating systems like Linux and OSX so they decided for the more conventional way for CoreCLR.
Update: DNX is now deprecated and replaced by DOTNET. Otherwise without invalidating this post content, just easier to use.
Is DNX an alternative to Mono? If not, then what will be the difference?
Mono is an open sourced development platform. Its implementation is based on the CLI specification, such as the platform that is provided by Microsoft. It includes a C# compiler, a runtime, a BCL and something called MCL (Mono Class Library, which is an extensions to the BCL). Mono itself can run on Linux, OS X, BSD and Windows on varying architectures.
DNX is an SDK containing all of the bits needed to build and run an application (including custom utilities such as the dnu
which is used to build and package the app), including the CLR (currently it deploys with CoreCLR). This CoreCLR can also be switched with Mono, which means it will be consuming all services of the Mono runtime, compiler, etc.
Mono as opposed to DNX provides the full platform (Runtime, BCL, JIT, etc.). DNX is used at the lowest level as the Native Process which invoked the CoreCLR. DNX would be used for scenarios such as self-host or building and running from the command line.
As @xanatos points out, DNX aspire to be able to ship the runtime with the application, where multiple runtimes will be able to live side by side without interfering each other.
Perhaps this image can clarify:
Here is the list which DNX can run on top (x86 showing twice as it is the default):
Active Version Runtime Architecture Location Alias
------ ------- ------- ------------ -------- -----
* 1.0.0-beta2-10735 clr x86 C:\Users\victorhu\.dnx\runtimes default
1.0.0-dev clr x64 C:\Users\victorhu\.dnx\runtimes clr-x64-dev
1.0.0-dev clr x86 C:\Users\victorhu\.dnx\runtimes clr-x86-dev
1.0.0-dev coreclr xd64 C:\Users\victorhu\.dnx\runtimes coreclr-x64-dev
1.0.0-dev coreclr x86 C:\Users\victorhu\.dnx\runtimes coreclr-x86-dev
1.0.0-dev mono C:\Users\victorhu\.dnx\runtimes mono-dev
There is an extensive wiki page explaning the DNX structure for more. @Will points out the ASP.NET docs page as well.
Update: 25/02/2016
DNX is now retired in favor of .NET CLI Tools.
Update: 8/6/2020
.NET CLI Tools are now retired in favor of dotnet sdk