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Difference between F-Droid clients
(feddit.de)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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The Basic one is still alpha. Its supposed to be a stripped down light weight version. I would say for now use the org.fdroid.fdroid if yoi are confused.