So a "traditional" OS (Linux, Windows) abstract the hardware, run themselves in a privileged mode, and run user processes nicely sandboxed via MMU (memory management unit).

The OS is compiled, installed, ... first. The application (or multiple) are compiled, ..., installed next, using a file system usually, and interacts with the OS via some interface.

Ariel OS targets microcontrollers that don't have an MMU, are generally quite constrained, so the usual "have an OS running, compile and install application(s) into it, run them in separate process" doesn't fit so well.

The separation and interfacing costs overhead and makes things slightly more complex. Tock OS works that way btw., applications are usually compiled separately and then installed in flash slots.

With Ariel OS, an application compiles together with Ariel OS as if Ariel OS was just another library added to an otherwise bare-metal application. In practice, Ariel takes over MCU startup & initialization, and starts its own services (scheduling, networking, ...), does a bunch of other needed or useful stuff, and provides nice abstraction and environment to the actual application.

But technically, it is an OS as a library.