Concurrency > In computer science, concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other.
Parallelism > Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently ("in parallel").
In my opinion there's really not that much more to concurrency that's hard, apart from safely organising the communication between concurrent processes/threads. It's then the opposite problem with parallelism; the difficulty is finding and implementing the physically separate execution of different threads of execution in a program, while (generally) the communication is seen as a concurrency problem.
In any case, I completely disagree with your idea that parallel systems must be concurrent. Concurrency arises completely due to the interactions between separate threads of execution, whether they be executing at the same time on separate processors, or scheduled one after the other on a single processor. This is why we have various process calculii (csp, pi-calculus etc), and things such as session types, in order to try and reason about it and manage it. Parallelism assumes nothing about the interactions between processes, only that they are assumed to be running on separate hardware.
As another poster mentioned, this fits fairly well with what the Haskell, Go, and general programming language research community considers to be the definitions of concurrency and parallelism. Look at any paper that focusses on concurrency, and you'll see it's about managing and making safe communication between separate processes. Look at a paper on parallelism, and it'll be on accelerating a parallelisable program on multicore or distributed hardware.
I also disagree with your assertion that the programming language research community disagrees with my definitions - I'm more of a systems person, but I do end up in their playground sometimes.
https://www.haskell.org/haskellwiki/Parallelism_vs._Concurre...
Consider, what does it mean to run parallel with something else? Means you are running a similar path. Not even necessarily at the same time. What does it mean to run concurrently with something else? Simply that you are running when it is.
My point is really that it is a lost cause to try and use such an outside common word to have a specific meaning.