Google `site:wikipedia.org` search (which also works in DuckDuckGo) uses Google's interface and index, i.e., you get a Google search results page. With Search Bangs, you get a search results page using that uses a websites own engine, e.g., it's filling out a search term with a template like `http://wikipedia.org/?search=*`.

This is actually very old idea that used to be implemented in various browsers and extensions. Here's a support page for Fireboxes implementation, which might still work[1]. Personally, I do this on OS X with LaunchBar Search Templates[2], which is nice because it's browser agnostic.

[1]: https://support.mozilla.org/en-US/kb/how-search-from-address...

[2]: https://www.obdev.at/resources/launchbar/help/SearchTemplate...

Bangs use the other site's built-in search engine, not DDG's index of that site.

"site:amazon.com" vs "!a" saves 13 characters.