Difference between "WSL2+docker desktop windows" and directly install docker on the WSL2 distro?

The main difference between using Docker Desktop with the WSL2 integration and using docker directly in WSL2 without Docker Desktop is the level of integration with your tools.

When you use Docker desktop, you have access to docker in powershell/cmd, have access to your file on windows, the possibility to switch to Windows container and to use it with your IDE.

If you install docker inside your WSL2 distro, docker will not be accessible from Windows directly.