git-core changed to git. git-core is now a dummy package

"git" is the proper name. see this thread for [context and history] (http://git.661346.n2.nabble.com/git-core-vs-git-package-on-ubuntu-td7576083.html):

Konstantin Khomoutov  Jan 25, 2013;
Git was packaged for Debian (and hence appeared in 
Ubuntu) when another package with the name "git" already existed in the 
archive, and was unrelated to Git.  So the Git package maintainer 
picked the name "git-core".  After that, the maintainers of both 
packages discussed this issue and the maintainer of the original 
package named "git" agreed to change the name of his package, and then, 
subsequently, "git-core" has been renamed to "git", and the "git-core" 
package has been turned into transitional dummy obsolete package. 

Now, whenever you're trying to install the "git-core" package, the 
package system tells you it's obsolete and suggests the "correct" 
package to install.  After some time (the next OS release or later), 
the "git-core" package will be removed completely from the archive. 

This is the standard way to handle such situations in Debian and its 
derivatives, so nothing special here.  The documentation on the 
whatever site you were referring to should probably be updated as 
git-core is obsolete even in the current stable release of Debian [1]. 
I'm not sure which LTS release of Ubuntu is currently supported, but 
you might check the state of the git-core package in it yourself, 
using [2].