Am not expert, but here's the understanding I've picked up:

When you use JavaScript through Node, your JS gets the ability to open files and make network sockets and so on, because there are a set of APIs implemented by Node and exposed to your JS code, like so:

JS <-> native APIs <-> Node implementation of platform-specific operations

WASI applies to WebAssembly instead of JS. So again if we're on Node:

wasm <-> native APIs (WASI) <-> Node implementation of platform-specific operations

But WASI is much more general than Node's APIs, and meant to be used by different engines in different environments (browsers, native bindings, etc).