Everything a site-search can do, plus Muse-exclusive features, of course.
You do not need to type the page names, the widget takes care of it for you automatically, and if you decided to exclude any page, simply type the page name/s and you are ready to go.
A powerful loading algorithm that allows your users to see the results live as they are being types, this is optional of course so you can choose to use this powerful feature. You can also assign any graphic to the search bar as the search trigger which may come handy on smaller devices.
No complicated styling option in a widget option panel, everything is made of text panels, change font, color, background, padding, and basically do whatever you can do on any text box, and do it individually for each part. It allows an easy customization.
Some users type "NIGHT", but you want them to search for "DAY", no problem, assign unlimited related-words, so it will be shown to the as suggestion at the bottom of the search results.
If you do not want your entire page to searched, use the powerful targeting options, choose to have, for example, only <h> tags to be searched, or the <p> tags, or to have a more targeted search, choose to have only certain text boxes to be searched by assigning them certain Paragraph Styles.