The way cores, processes, and threads work exactly?

Cores (or CPUs) are the physical elements of your computer that execute code. Usually, each core has all necessary elements to perform computations, register files, interrupt lines etc.

Yes, threads and processes can run concurrently on multi-core CPUs, so this works as you describe (regardless of how you create those threads and processes, OpenMP or otherwise). A single process or thread only runs on a single core at a time. If there are more threads requesting CPU time than available cores (generally the case), the operating system scheduler will move threads on and off cores as needed.

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