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 a few choices for Ubuntu in the Window Store.

• Just "Ubuntu": This will always be the latest stable, LTS version.
• Ubuntu 22.04 LTS: For developers who want version 22.04 specifically.
• Ubuntu 20.04.4 LTS: For developers who want version 20.04 specifically.
• Ubuntu 18.04.5 LTS: For developers who want version 18.04 specifically.

If you installed the plain "Ubuntu" app (with no version number) before 20.04 or 22.04 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 current Ubuntu packages to latest

sudo do-release-upgrade    # perform an upgrade to Ubuntu 22.04

Follow all prompts and heed all warnings. They are usually due to customization 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.

Disclaimer: This following procedure requires a pre-installed GNU/Linux Distributions in WSL (like OP has Ubuntu 16.04 already installed). The provided links may not work in future. You may comment below if any. It requires little knowledge of GNU/Linux command line tools e.g. tar, UnsquashFS etc. Install these tools before following this procedure.

• Installer Executable: You need an executable importing WslRegisterDistribution function which installs the distribution. There are two ways. You can compile your own installer from source code (link1) or extract the installer from Microsoft provided Appx package(link2).

• Get Ubuntu 18.04: Download the Ubuntu 18.04 SquashFS file. Now run old Ubuntu with WSL in that download folder and login as root user. Run the following commands below (only with root user):

cp ./ubuntu-18.04-server-cloudimg-amd64.squashfs ~ 
cd ~ 
unsquashfs -d temp ubuntu-18.04-server-cloudimg-amd64.squashfs 
cd temp 
tar -czf ../Ubuntu.tar.gz --hard-dereference * 
cd .. 
mv Ubuntu.tar.gz /mnt/c 

The cp command copies the SquashFS file in home directory (required). UnsquashFS extracts files in temp folder and tar compresses all the files in a .tar.gz format. Then mv command move that file in previous download folder. You may delete the temp folder with rm -rf ~/temp command.

• Install: Place both the executable and tar.gz file in same folder where you want to install. You've to run a command (link1) or double click on the executable (link2) to install. It requires 15-30 seconds to install depending on you machine.