Firefox was automatically updated to version 14 a few days ago through update manager, but Chromium web browser is still stuck in version 18 while Google Chrome is already in version 20. Why does this happen and how can I update my Chromium to a more recent version?
In a Linux distribution, software doesn't usually use its own internal "automatic update" mechanism. Instead, it relies on the distribution to update it.
This is the case for both Firefox and Chromium supplied with Ubuntu.
The interesting thing here is that Firefox and Chromium have a different level of support from Canonical, and also that Firefox on Ubuntu has a somewhat unusual release strategy.
Firefox is included in Ubuntu's main repository, whereas Chromium is in the universe repository. This means that Ubuntu's version of Firefox receives the best level of support directly from Canonical, whereas Chromium's support relies on the Ubuntu community. Most packages in universe rely heavily on the work of Debian developers, and Debian has different priorities. So, based on this you would expect Firefox to include more Ubuntu-specific customisation, and to be better supported with updates.
The thing is, almost all software in a stable-release distribution (like Ubuntu, and most other distributions other that the "rolling release" ones) should not receive updates to new versions of software during the life cycle of that version of the distribution. At best, it should receive only minor updates or security patches. Firefox on Ubuntu is somewhat unusual here, because Ubuntu are providing full major new upstream versions of Firefox to their stable distributions.
The justification for this will be Firefox's rapid release strategy, which ensures that "major" releases are actually somewhat less disruptive than most software's major releases, but also makes it quite hard to backport security patches to older versions. So Canonical has obviously decided just to give Ubuntu the new upstream version than patch the old version.
For Chromium, it's not completely like this, but looks can be deceiving. Chromium on Ubuntu sometimes does get new upstream releases (which is why even Lucid is on a v18.x), and other times the Ubuntu community patch the existing version with fixes and security updates, but don't increment its version number. However, this means that despite the version number of Chromium in Ubuntu, it still includes some of the fixes that newer versions of Chromium have.
No the project isn't dead. The Ubuntu Chromium Team just doesn't have enough people working on it, that's why the Ubuntu packages are out of date. Benjamin Kerensa is currently reaching out to new developers to support the team here. So the situation will hopefully improve soon.
Ubuntu's version of Chromium is maintained by the Ubuntu developers. So after the Chromium developers update, Ubuntu developers then take a look at it to see how it works with Ubuntu and makes any necessary modifications. This is the only advantage to using Chromium over Chrome. To use Chrome on Ubuntu, you have to download the version from Google and trust that they made it work properly with Ubuntu.
If you'd rather get the latest version, without regard for whether it's been approved by Ubuntu developers, then you should just use Chrome.
The Chromium project lives here, with builds for Windows, Linux, iOS, Android etc.
From the releases page, latest appears to be version 22. Not sure why launchpad.net doesn't have it.