A search link stores a query in a link that takes you to live search results for that stored search. They're found on user pages and talk pages. Use one to bring the full feature set of MediaWiki Search, or features of external search engines, to bear on users unfamiliar with their search parameters.
One type of search link is a wikilink with all the capabilities of Search (search box), and with standard wikilink syntax: [[Special:Search/query| label]]. So this search link will (1) navigate: [[Special:search/Wales]] → Special:search/Wales or (2) search: [[Special:search/~Wales | search/~Wales]] → search/~Wales if you prefix a ~ tilde character.
All other search links are made from a template that will build a URL instead of wikilink. A URL can for example can call off-site search engines to search Wikipedia.
{{Search link}} offers all the capabilities of Searching (search box), plus extra (URL) parameters for combinations of namespaces, and where you can escape the 20-results-per page-limitation, shareable: {{search link | et al | ''label'' | ns4 | ns5 | limit = 123}} → label.
{{Template usage}} – develop a template regex search, and pinpoint specific template-call details. {{Template usage | Convert | \{{!}}C\{{!}}F | 0 | Articles that convert Celsius to Fahrenheit}} → Articles that convert Celsius to Fahrenheit
{{ShortSearch}} – create three search links: {{ShortSearch | system operations research}} → WPGWPG (search Wikipedia, "Google" Wikipedia, and Google search)