Dart compiles to JavaScript, is open source, and is now in ECMA. The project has mostly Google engineers committing, but we also have plenty of open-source contributions.
asm.js is a compile target that takes C/C++ code and outputs lots of typed arrays, and a custom engine to interpret the asm.js "hints". It's an interesting way to get C code onto the web, but developers don't write asm.js code by hand. In contrast, Dart is designed to be written by developers. The similarity is that both asm.js and Dart want to enable faster experiences for users, but they take very different approaches.