I personally prefer to call this asynchronous computing broken into parallel (execute at the same time) and concurrent (execution is interleaved) models.
Asynchronicity is just how sequential models are extended to support concurrency. Parallelism and concurrency are orthogonal, so a concurrent model can be executed in parallel.
> Asynchronicity is just how sequential models are extended to support concurrency.
Asynchronicity just means not existing or occurring at the same time, i.e. not synchronised or without synchronisation.
How you expand that definition to computer science is a matter of opinion. I personally take the opinion that an asynchronous operation could be either concurrent or parallel.
> Parallelism and concurrency are orthogonal, so a concurrent model can be executed in parallel.