A search engine is software which builds a database of web pages, indexed by keywords. End-users see an interface which returns lists of web pages, in response to keywords entered by a user.
From the mid-90s to the mid-2000s, many search engines and indexes arose on the web. They died or consolidated into just a handful of true engines. There are several front-ends, though. For example, Yahoo uses Bing.
In today's parlance, a web index is a manually curated list of websites.
An archive is a collection of materials deemed especially valuable.
For example, the Internet Wayback machine, aka WABAC, takes snapshots of web pages over time. It lets you see old versions of websites, even websites that have since Disappeared.
A portal abstracts content from other websites, organizes it under a common theme, and presents the collected results.