Can I upgrade my existing Ubuntu installation in WSL from 16.04 to 18.04?

I just forced an upgrade from 16.04 and it was successful, though the process was not all well.

sudo do-release-upgrade -d

First do the upgrade. As people have reported in comments, it's likely all that you need to do before 18.04 is all set up. In a few cases like mine, it will do most of the things while showing as "failed".

In case it shows as "failed", open /etc/apt/sources.list and replace all "xenial" with "bionic", and sudo apt update && sudo apt -y upgrade. Most people should have everything done at this point.

In some cases (but not all), APT and Debian Packager may fail during the process. According to this GitHub thread, you need to remove grub and kernels, if present:

sudo apt -f purge grub-pc
sudo apt -f purge linux-image*

Repeat the last command several times as dpkg will fail after removing every package. After all those Linux images are removed, you get a fully working Bionic Beaver in your WSL.

Read more: A Guide to Upgrading your Ubuntu App’s Release – Windows Command Line Tools For Developers

Yes, you can!

There are now three varieties of Ubuntu available on the Window Store.

• Ubuntu: This will always be the latest stable, LTS version.
• Ubuntu 20.04 LTS: For developers who want version 20.04 specifically.
• Ubuntu 18.04 LTS: For developers who want version 18.04 specifically.

If you installed the plain "Ubuntu" app (with no version number) before 20.04 was made available on the Windows Store, you may upgrade it with the following set of commands:

sudo apt update -y         # makes apt system itself up-to-date 
sudo apt dist-upgrade -y   # updates Ubuntu 18.04 packages to latest

sudo do-release-upgrade    # performs the upgrade to Ubuntu 20.04

Follow all prompts and heed all warnings you are presented with. They are usually due to customizations and third-party libraries or repositories you added yourself.

Official source: https://devblogs.microsoft.com/commandline/upgrading-ubuntu/

There is official Ubuntu18.04 in the windows store now, as well as Ubuntu16.04.

Though I haven't found any official information what is the difference between these two and the Ubuntu.

Yes, there are three different Ubuntu in windows store at the moment.