> there is no guarantee in the API that they both happen literally simultaneously

There's no actual guarantee in the API that if you spawn multiple threads and call blocking network I/O that those happen literally simultaneously. Maybe the OS has a big mutex on network I/O to serialise them.

Of course, that's not what happens in practice. But neither is it what happens, in practice, to async network APIs called concurrently in one thread. So I don't think that can be the difference between concurrent and parallel.

concurrent programs enable parallel evaluation. concurrency is necessary but not sufficient for parallelism.