What are the differences between Search API/Views and regular Views? What are the differences between setting up Search API (with the Search Views module) and creating a particular set of results with Search Views against using Views is the normal manor?

The big difference I can see straight away is the Search Facets and being able to easily create the blocks that filter/facet the search results.
This question is pretty vague and probably should be blocked.. but I'll take a stab at it.

Search API views have a bunch of different features.  They allow full text search across multiple fields.  E.g. title and body and possible extra text fields all combined in one search filter.

You can set your search api setting to also deal with stemming (e.g. search for learn and also get learning, learns, and the like.

Search API views also allow you to sort by Relevancy.  E.g., if the search terms are found more times, the relevancy is higher.  You can also set up boosts for different fields.  E.g. if the term is in the title or product fields, it has a score of 10 rather then in the body where it has a score of 0.5. 

This allows you more control over what shows up at the top of the search.

Search API views can also be set up to return 'excerpts' from the content with the search terms highlighted.  This can be useful in helping people decide if the content is what they want.

There are a bunch of other things that Search API / Views can do, like synonym setups (e.g. orthopedic is the same as orthopaedic).  Weighting specific nodes higher. Many of them may be at the search engine level (e.g. Solr) or require some extra modules (DB Server).

There is also the possibility of setting up auto completion suggestions as well.