[git] Do Git tags only apply to the current branch?

When calling just git tag <TAGNAME> without any additional parameters, Git will create a new tag from your current HEAD (i.e. the HEAD of your current branch). When adding additional commits into this branch, the branch HEAD will keep up with those new commits, while the tag always refers to the same commit.

When calling git tag <TAGNAME> <COMMIT> you can even specify which commit to use for creating the tag.

Regardless, a tag is still simply a "pointer" to a certain commit (not a branch).