I don't like the essential characteristic of concurrency being nondeterminism. its really that multiple processes are running concurrently. if we don't have serializing operations, we have arbitrary execution order. but if we do then we can introduce the necessary determinism while still being (largely) concurrent in evaluation. and if those logically concurrent processes are physically concurrent then we have parallelism. so the first is necessary but not sufficient for the latter.
so I find saying that we have one or the other to pretty misleading.