Chromium is the name given to the open source project and the browser source code that was released and maintained at www.chromium.org. One can compile this source code to get a fully working browser.
Google takes this source code, and adds on the Google name and logo, an auto-updater system called GoogleUpdate, and RLZ1 , and calls this Google Chrome. As such, everything which applies to Chromium below also applies to Google Chrome, while there are some things that apply to Google Chrome (such as the auto-updater) that do not apply to Chromium.
If you are on Linux and looking for specific differences check THIS
For full discussion check this
1. When you do a Google search from the Google Chrome address bar, an
"RLZ parameter" is included in the URL. It is also sent separately on
days when Google Chrome has been used or when certain significant
events occur such as a successful installation of Google Chrome. RLZ
contains some encoded information, such as where you downloaded Google
Chrome and where you got it from. This parameter does not uniquely
identify you, nor is it used to target advertising. This information
is used to understand the effectiveness of different distribution
mechanisms, such as downloads directly from Google vs. other
distribution channels. This cannot be disabled so long as your search
provider is Google. If your default search provider is not Google,
then searches performed using the address bar will go to your default
search provider, and will not include this RLZ parameter.
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