The docker engine is the daemon. Docker Desktop comes with a convenient UI to allow developers to start/stop Docker Desktop (and with it the backend that runs inside the utility vm that runs the docker engine). It is not meant to be used for 24/7 operations.
To run Linux containers, the docker engine must be run on a Linux system, as docker depends on Linux kernel, libraries, and tools. You can install docker-ce on any supported Linux system / architecture. On Windows you would need to create a Linux vm, and install docke-ce following the installation instructions. It is possible to run docke-ce in a WSL2 distribution as long as the OS / architecture is in the support matrix and systemd is enabled for the WSL2 distribution.