After successfully installing Docker in WSL, if I run standard Docker commands, I get connection errors. Runing with sudo or not yields the same result in all examples.
The Docker daemon can't run under WSL as it doesn't implement the necessary kernel ABI's. If you're running Docker for Windows, you are probably connecting to the Hyper-V virtual machine that it manages.
Because it's on a different machine, you will not be able to mount WSL directories as Docker volumes, but you can build images from a WSL directory. This is because on a build, the client creates a tarball and sends it to the daemon.