When I search for Chromium in Ubuntu Software on Ubuntu 16.04, There are 2 options.
Which one should I select?
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The first and the third items are both the Chromium browser. The former is a snap package and the latter is a Debian package.
You can confirm this from the version numbers and descriptions. The first:
$ snap search chromium Name Version Developer Notes Summary chromium 62.0.3202.75 canonical - Chromium web browser, open-source version of Chrome
$ apt search chromium-browser Sorting... Done Full Text Search... Done chromium-browser/xenial-updates,xenial-security 62.0.3202.75-0ubuntu0.16.04.1313 amd64 Chromium web browser, open-source version of Chrome
and the AppStream description:
$ appstreamcli search chromium Identifier: chromium-browser.desktop [desktop-application] Name: Chromium Web Browser Summary: Access the Internet Package: chromium-browser Icon: chromium-browser_chromium-browser.png
gnome-software command should help. Both of these commands open the third entry:
gnome-software --details=chromium-browser.desktop gnome-software --details-pkg=chromium-browser
chromium-browser.desktop is the AppStream ID, and
chromium-browser is the package name.