Shortcuts are wikilinked on community pages, talk pages, and edit summaries, but not in mainspace articles. Transclusions in mainspace are common and do not need to be "fixed".
From a different spelling: This is a redirect from a title with a different spelling of the target name. Pages that link to this redirect may be updated to link directly to the target page if that results in an improvement of the text. Do not "fix" such links if they are not broken. Also, these links with piped links.
Please note that there are many more specific templates. See subcategories of Category:Redirects from modifications for other options (capitals, abbreviations, diacritics, plurals, stylizations, transliteration, ligatures, different parts of speech, etc.)
From a page move: This is a redirect from a page that has been moved (renamed). This page was kept as a redirect to avoid breaking links, both internal and external, that may have been made to the old page name.
When appropriate, protection levels are automatically sensed, described and categorized.