The 2 terms have been used inconsistently in the past and some authors have even alternated between them during their lifetime.
I prefer the view where "concurrent" processes (a.k.a. tasks a.k.a. threads) are those where the execution of their parts is done in an unpredictable order, i.e. they can be interleaved in an unpredictable order.
For the correctness of programs, it only matters whether some things are executed sequentially or concurrently. If they are executed concurrently, whichever order of execution happens must not change the results in any way.
For correctness, it does not matter whether in reality all the concurrent processes are executed by a single hardware thread, so none of them are ever executed simultaneously in time, or all the processes are executed in parallel, on different processor cores.
For correct concurrent programming, what matters is how the access to shared resources is controlled, using either mutual exclusion, or optimistic accesses with retries when necessary, or dynamic partitioning of the shared resource (i.e. of an array or of a queue) into disjoint parts that allow concurrent accesses.
Parallelism only matters for the achievable performance of a program. To enable parallel execution for increased performance, there are also specific programming techniques that are required, for minimizing the dependencies that force serial execution, i.e. data dependencies a.k.a. functional dependencies, flow-of-control dependencies and resource dependencies a.k.a. operational dependencies.
Something that can cause confusions between concurrency and parallelism is the difference between the program written by the programmer and how it is really executed by a modern CPU.
When the programmer writes a program that describes multiple concurrent processes, a CPU may easily execute all of them in parallel. But even when the programmer writes only a sequential program, a modern CPU with out-of-order execution will analyze the program, identify the dependencies between instructions and convert the sequential program into a set of concurrent processes that will be executed in parallel by separate hardware execution units, if possible, though they may also be executed sequentially on a single execution unit, when the others are busy.
Thus even when the programmer does not write a concurrent program, it may still have parts that are executed in parallel, but that is not parallelism without concurrency, the concurrency is introduced by the hardware scheduler, which identifies shared resources and any other dependencies that could inhibit the transformation of the sequential program into a concurrent program.