Do Git tags only apply to the current branch?

CharlesB's answer and helmbert's answer are both helpful, but it took me a while to understand them. Here's another way of putting it:

• A tag is a pointer to a commit, and commits exist independently of branches.
  • It is important to understand that tags have no direct relationship with branches - they only ever identify a commit.
    • That commit can be pointed to from any number of branches - i.e., it can be part of the history of any number of branches - including none.
  • Therefore, running git show <tag> to see a tag's details contains no reference to any branches, only the ID of the commit that the tag points to.
    • (Commit IDs (a.k.a. object names or SHA-1 IDs) are 40-character strings composed of hex. digits that are hashes over the contents of a commit; e.g.: 6f6b5997506d48fc6267b0b60c3f0261b6afe7a2)

• Branches come into play only indirectly:
  • At the time of creating a tag, by implying the commit that the tag will point to:
    • Not specifying a target for a tag defaults to the current branch's most recent commit (a.k.a. HEAD); e.g.:
      • git tag v0.1.0 # tags HEAD of *current* branch
    • Specifying a branch name as the tag target defaults to that branch's most recent commit; e.g.:
      • git tag v0.1.0 develop # tags HEAD of 'develop' branch
    • (As others have noted, you can also specify a commit ID explicitly as the tag's target.)
  • When using git describe to describe the current branch:
    • git describe [--tags] describes the current branch in terms of the commits since the most recent [possibly lightweight] tag in this branch's history.
    • Thus, the tag referenced by git describe may NOT reflect the most recently created tag overall.

If you create a tag by e.g.

git tag v1.0

the tag will refer to the most recent commit of the branch you are currently on. You can change branch and create a tag there.

You can also just refer to the other branch while tagging,

git tag v1.0 name_of_other_branch

which will create the tag to the most recent commit of the other branch.

Or you can just put the tag anywhere, no matter which branch, by directly referencing to the SHA1 of some commit

git tag v1.0 <sha1>