Yes? Parallelism is inherently concurrent but concurrency is not inherently parallel. But single core concurrency still exists as a form of non-parallel concurrency.
The point I'm trying to make is down to brass tacks, single core concurrency is a lot simpler than multi core concurrency, because you don't need any hardware cooperation.
Before you were saying they are two different things, now you're saying they are the same when you have multiple cores and not the same when you have a single core. If they're the same when you have multiple cores, isn't there just single and multi-core concurrency by your own definitions? If so, why are you making a distinction of parallelism and concurrency?
Parallelism is a physical thing, concurrency is a logical thing.
So by your own definition, wouldn't multi-core concurrency be parallelism?