From a related word or phrase: This is a redirect from a word or phrase (term) to a page title that is related in some way. This redirect might be a good search term, or it could be a candidate for a Wiktionary link.
Redirects from related words are not properly redirects from alternative spellings of the same word. They are also different from redirects that are subtopics or related topics, because unlike those, a related word or phrase probably does not warrant its own subtopic section in the target page or possess the possibility of ever becoming an article, template, project page, and so forth.
From an alternative name: This is a redirect from a title that is another name or identity such as an alter ego, a nickname, or a synonym of the target, or of a name associated with the target.
This redirect leads to the title in accordance with the naming conventions for common names to aid searches and writing. It is not necessary to replace these redirected links with a piped link.
If this redirect is an incorrect name for the target, then {{R from incorrect name}} should be used instead.
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.