So is WebAssembly: you'd compile your code to a .wasm file "offline". In both cases, you compile your code to a bytecode format, which the browser then compiles (directly or via JS polyfill) to native code.

A key part of WebAssembly's strategy is a polyfill that runs on the client and generates appropriate JS (asm.js or otherwise).

Right, there will be a wasm.js polyfill just like pepper.js, for browsers without native support. And once browsers have native support, that polyfill can be dropped.

The difference between PNaCl and WebAssembly is simply that WebAssembly doesn't come with a pile of API expectations established by a single browser, and that it has the blessing of multiple browser vendors. Ignoring the API, the latter could have worked with PNaCl just as well.