Concurrency is writing code with the appearance of multiple linear threads that can be interleaved. Notably, it's about writing code. Any concurrent system could be written as a state machine tracking everything at once. But that's really hard, so we define models that allow single-purpose chunks of linear code to interleave and then allow the language, libraries, and operating system to handle the details. Yes, even the operating system. How do you think multitasking worked before multi-core CPUs? The kernel had a fancy state machine tracking execution of multiple threads that were allowed to interleave. (It still does, really. Adding multiple cores only made it more complicated.)
Parallelism is running code on multiple execution units. That is execution. It doesn't matter how it was written; it matters how it executes. If what you're doing can make use of multiple execution units, it can be parallel.
Code can be concurrent without being parallel (see async/await in javascript). Code can be parallel without being concurrent (see data-parallel array programming). Code can be both, and often is intended to be. That's because they're describing entirely different things. There's no rule stating code must be one or the other.