A Wiki Page Library is a document library set up to hold Wiki Pages. It includes the methods for automatically creating pages based on Wiki Links in the content, as well as the custom views for recent additions, etc... You can create a Wiki library in any SharePoint site, but it is accessed like any other document library - via Quick Launch.
A Wiki Site is a SharePoint Site which has its default page automatically redirected to the home page of the Wiki Page library created in that site, making it look like the entire site is a Wiki. You can still add other lists and document libraries
to the site, but the home page is always the Wiki home.