When you use a Search Engine, you submit specific words or phrases and their computer will return the URLs of web pages that contain those words or phrases. An Index works more like the 'yellow pages' or a table of contents; you look up the category in which you are interested and then move to sub-categories and then to individual web sites.
The big difference is that a dumb old computer can collect the data for a Search Engine while it takes a person to figure out where a site goes in an Index.
Of course, lately, the indexes seem to be transforming into portal sites (sites people set up as their start pages which offer a variety of services).
Search Engines
Looking for something specific on the Web; try using a 'virtual library'.