How is a tag different from a branch in Git? Which should I use, here?

If you think of your repository as a book that chronicles progress on your project...

Branches

You can think of a branch as one of those sticky bookmarks:

A brand new repository has only one of those (called master), which automatically moves to the latest page (think commit) you've written. However, you're free to create and use more bookmarks, in order to mark other points of interest in the book, so you can return to them quickly.

Also, you can always move a particular bookmark to some other page of the book (using git-reset, for instance); points of interest typically vary over time.

Tags

You can think of tags as chapter headings.

It may contain a title (think annotated tags) or not. A tag is similar but different to a branch, in that it marks a point of historical interest in the book. To maintain its historical aspect, once you've shared a tag (i.e. pushed it to a shared remote), you're not supposed to move it to some other place in the book.

A tag represents a version of a particular branch at a moment in time. A branch represents a separate thread of development that may run concurrently with other development efforts on the same code base. Changes to a branch may eventually be merged back into another branch to unify them.

Usually you'll tag a particular version so that you can recreate it, e.g., this is the version we shipped to XYZ Corp. A branch is more of a strategy to provide on-going updates on a particular version of the code while continuing to do development on it. You'll make a branch of the delivered version, continue development on the main line, but make bug fixes to the branch that represents the delivered version. Eventually, you'll merge these bug fixes back into the main line. Often you'll use both branching and tagging together. You'll have various tags that may apply both to the main line and its branches marking particular versions (those delivered to customers, for instance) along each branch that you may want to recreate -- for delivery, bug diagnosis, etc.

It's actually more complicated than this -- or as complicated as you want to make it -- but these examples should give you an idea of the differences.

From the theoretical point of view:

• tags are symbolic names for a given revision. They always point to the same object (usually: to the same revision); they do not change.
• branches are symbolic names for line of development. New commits are created on top of branch. The branch pointer naturally advances, pointing to newer and newer commits.

---

From the technical point of view:

• tags reside in refs/tags/ namespace, and can point to tag objects (annotated and optionally GPG signed tags) or directly to commit object (less used lightweight tag for local names), or in very rare cases even to tree object or blob object (e.g. GPG signature).
• branches reside in refs/heads/ namespace, and can point only to commit objects. The HEAD pointer must refer to a branch (symbolic reference) or directly to a commit (detached HEAD or unnamed branch).
• remote-tracking branches reside in refs/remotes/<remote>/ namespace, and follow ordinary branches in remote repository <remote>.

---

See also gitglossary manpage:

branch

A "branch" is an active line of development. The most recent commit on a branch is referred to as the tip of that branch. The tip of the branch is referenced by a branch head, which moves forward as additional development is done on the branch. A single git repository can track an arbitrary number of branches, but your working tree is associated with just one of them (the "current" or "checked out" branch), and HEAD points to that branch.

tag

A ref pointing to a tag or commit object. In contrast to a head, a tag is not changed by a commit. Tags (not tag objects) are stored in $GIT_DIR/refs/tags/. [...]. A tag is most typically used to mark a particular point in the commit ancestry chain.

tag object

An object containing a ref pointing to another object, which can contain a message just like a commit object. It can also contain a (PGP) signature, in which case it is called a "signed tag object".

What you need to realize, coming from CVS, is that you no longer create directories when setting up a branch.
No more "sticky tag" (which can be applied to just one file), or "branch tag".
Branch and tags are two different objects in Git, and they always apply to the all repo.

You would no longer (with SVN this time) have to explicitly structure your repository with:

branches
   myFirstBranch
     myProject
       mySubDirs
   mySecondBranch
     ...
tags
   myFirstTag
     myProject
       mySubDirs
   mySecondTag
   ...

That structure comes from the fact CVS is a revision system and not a version system (see Source control vs. Revision Control?).
That means branches are emulated through tags for CVS, directory copies for SVN.

Your question makes senses if you are used to checkout a tag, and start working in it.
Which you shouldn't ;)
A tag is supposed to represent an immutable content, used only to access it with the guarantee to get the same content every time.

In Git, the history of revisions is a series of commits, forming a graph.
A branch is one path of that graph

x--x--x--x--x # one branch
    \ 
     --y----y # another branch
       1.1
        ^
        |
        # a tag pointing to a commit

• If you checkout a tag, you will need to create a branch to start working from it.
• If you checkout a branch, you will directly see the latest commit it('HEAD') of that branch.

See Jakub Narębski's answer for all the technicalities, but frankly, at this point, you do not need (yet) all the details ;)

The main point is: a tag being a simple pointer to a commit, you will never be able to modify its content. You need a branch.

---

In your case, each developer working on a specific feature:

• should create their own branch in their respective repository
• track branches from their colleague's repositories (the one working on the same feature)
• pulling/pushing in order to share your work with your peers.

Instead of tracking directly the branches of your colleagues, you could track only the branch of one "official" central repository to which everyone pushes his/her work in order to integrate and share everyone's work for this particular feature.