Example: python allows concurrency but not parallelism. Well not really though, because there are lots of examples of parallelism in python. Numpy both releases the GIL and internally uses open-mp and other strategies to parallelize work. There are a thousand other examples, far too many nuances and examples to cover here, which is my point.
Example: gambit/mit-scheme allows parallelism via parallel execution. Well, kindof, but really it's more like python's multiprocess library pooling where it forks and then marshals the results back.
Besides this, often parallel execution is just a way to manage concurrent calls. Using threads to do http requests is a simple example, while the threads are able to execute in parallel (depending on a lot of details) they don't, they spend almost 100% of their time blocking on some socket.read() call. So is this parallelism or concurrency? It's what it is, it's threads mostly blocking on system calls, parallelism vs concurrency gives literally no insights or information here because it's a pointless distinction in practice.
What about using async calls to execute processes? Is that concurrency or parallelism? It's using concurrency to allow parallel work to be done. Again, it's both but not really and you just need to talk about it directly and not try to simplify it via some broken dichotomy that isn't even a dichotomy.
You really have to get into more details here, concurrency vs parallelism is the wrong way to think about it, doesn't cover the things that are actually important in an implementation, and is generally quoted by people who are trying to avoid details or seem smart in some online debate rather than genuinely problem solving.