See Mercurial <=> Git Command comparison

git branch shows existing local branches, while git branch -r causes the „remote-tracking“ branches to be listed, and option -a shows both. See git-branch

With Git it is not possible to directly swich to a different branch on a cloned repository like in Mercurial. Instead first you have to create a new (local) branch wich „tracks“ the specified remote brach, eg. (origin/stable) and then checkout (=update) this branch to your working directory. The following command does both steps at once:

git checkout -b stable origin/stable

Now you can pull all needed updates whenever a new release is made:

git pull

See also

• Probably good intro
• Mercurial Tips — Subversion Tips — CVS Tips
• man gittutorial
• Git User's Manual