Web or Internet search engines look for entered keywords in a web site index. A web crawler finds information to put into the index file. Most search engines have a lot in common but may have some differing features (algorithms) - types of pages or files it can target, how the engine searches the index for the entered keywords, and ranking systems to determine the order of the results based on relevance.
Subject directories are human driven rather than automated. Based on standard selections criteria, volunteers or staff review and select content. Usually web sites are described, tagged or annotated. Subject directories can be browsed or searched.
Did your professor tell you to use only websites with a .gov or .edu or other limited domains? The advanced search feature in Google will allow you to limit results to only pages from government or education organizations.
For Google and most other search engines, you can enter your search terms and include the following string of characters, site:edu. In place of "edu," you could also put "org," "mil," or "gov."
Metasearch engines don't have their own web index, but search many different indexes from third party search companies. Metasearching allows comparison of results between search engines and helps the user to avoid missing results that might be left out when using only one engine.