The two projects are really similar no doubt. I can't speak for AssemblyScript, but my own motivation was simple. I wanted to learn WebAssembly and I wanted an accessible platform to do so with. At the time this wasn't really possible, tools like emscripten took forever to set up and were clunky to use. Plus I knew C already, I wanted to learn WebAssembly instead.
So where Walt is an attempt to write WebAssembly with a familiar syntax, AssemblyScript is an attempt to compile TypeScript to WebAssembly. To do so AssemblyScript comes with many more niceties/features out of the box IIRC, like optional(?) GC for example. Walt makes no such attempts and takes a more DIY approach.
Walt also has language extensions, via customizable syntax and compiler pipeline, where AssemblyScript is a TypeScript compiler more or less. My hope is that this allows for a babel-like situation for WebAssembly in the future via the tooling setup for Walt. I don't think this is a goal of AssemblyScript.