It's complicated.

Now there's the "pure" HarmonyOS (previously known as HarmonyOS NEXT) that most recent Huawei phones now have preinstalled (at least as an option for foreign markets). It doesn't have AOSP or Linux kernel and thus no compatibility. It just runs native apps (HAP).

Then, historically there's also a commercial version based on AOSP but removed Google services. You could buy it in a store back then, and it's compatible with Android apps that don't require Google services (up to a certain version?) Most Chinese apps don't rely on Google services in the first place.

There's also the open source version OpenHarmony. It was never commercially available. It uses the Linux kernel without AOSP. I believe part of it was used for the pure HarmonyOS development. It's said that the micro-kernel architecture was preserved for the pure HarmonyOS, which is quite interesting.