What is the difference between base, core, extra and community systems when installing the Arch-Linux?
pacstrap /mnt base
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You are confusing a couple different concepts here.
base is a package group. It's what many consider to be the “default” package set for an Arch Linux install (and many of the rest of Arch will assume that you have all of the packages in
base installed—so this isn't really an incorrect assertion).
On the other hand,
community are repositories. It is not too surprising that these can be confused with package groups (since repos are just large sets of packages). But package groups are meant to associate particular packages with one another (e.g., the
gnome group contains packages related to GNOME). Repositories just store packages.
core contains packages that are central to the running of a Linux distribution. You should probably expect to have almost all of its packages installed. For example, I have about ⅔ of them installed on my machine.
extra are packages that are widely used in running a Linux machine but will not be absolutely necessary for keeping a stable system. For example, you will find
core) because headless machines do not need X.
community is a bit of a different beast. Where
extra are maintained by the Arch Developers,
community is maintained by the Arch Trusted Users. This group of users maintains the AUR and moves things into
community as they (and the community at-large) see fit.
There are other repositories as well (most notably
multilib and the
testing repositories), but not all users will want them enabled. In addition, you can easily create your own repository (which is one of the best decisions I have ever made) that you can host locally with a tool called
repose. Additionally, there are some Unofficial User Repositories.
Some additional reading: