a branch of historical linguistics that is concerned with comparing languages to establish their historical relatedness.
Of the three questions tagged
[comparative-linguistics], none is really about this type of diachronic study of languages. (Only What metrics can be used to gauge language similarity? can be made relevant to comparative linguistics, but the methods it asks about are usually synchronic methods.)
A better tag for these three questions would be contrastive linguistics, which has often been linked to issues of applied linguistics.
We also have a language-comparison tag, which does not have questions about the historical relatedness of languages. Most questions tagged
[language-comparison] are about the impact of language distance (or similarity) on the difficulty of learning a specific language. The tag
[contrastive-linguistics], if it existed, would also be a fairly good fit for these questions.
One way to solve this issue is to create the tag
[contrastive-linguistics] (proposed description: "Questions about differences and similarities between two or more languages.") and retag all questions with
[contrastive-linguistics]. Then give [comparative-linguistics] the following description: "Questions about the historical relatedness between languages that are relevant to language learning and teaching" (if they aren't relevant to language learning and teaching, they should be moved to Linguistics SE). Strictly speaking, the
[language-comparison] tag can be replaced by
[contrastive-linguistics], but some people may want to keep it because it is easier to understand.
Update 2 (30.09.2016): the tag comparative-linguistics has been removed from two question where it did not apply.