The point of both projects is to allow a larger class of programs (and programming languages) to run on web platforms.
The point of PNaCl was to overcome or remove some of the constraints that come with the JavaScript language, like the lack of a concurrency model. This necessitates a new runtime. Since a new runtime was required anyways, Google decided to expend the engineering effort to make it as similar to native code as possible in terms of capabilities and performance, while also maintaining security.
The point of asm.js was to not include another runtime in the browser, but still meet the needs of the programs that PNaCl was trying to serve. Because it plays within the bounds of JavaScript it doesn't meet all the needs that PNaCl does (again, like concurrency), but it still allows native-like programming.
The point of PNaCl was to overcome or remove some of the constraints that come with the JavaScript language, like the lack of a concurrency model. This necessitates a new runtime. Since a new runtime was required anyways, Google decided to expend the engineering effort to make it as similar to native code as possible in terms of capabilities and performance, while also maintaining security.
The point of asm.js was to not include another runtime in the browser, but still meet the needs of the programs that PNaCl was trying to serve. Because it plays within the bounds of JavaScript it doesn't meet all the needs that PNaCl does (again, like concurrency), but it still allows native-like programming.