Google's index is the crawling information they gathered. You can actually do searches and get results as they would have been 7 years ago. The WayBack Machine just caches the HTML pages and would not provide this functionality.

Briefly in 2004, the Wayback Machine provided a search engine for its entire archive, back to about 1997. This is now gone. Probably Amazon didn't like it (Amazon owns Alexa and thus controls the WM caching).