I think that intitle: is an or operator - ie, hosting or design in the title allintitle: is an and operator - ie, hosting and design in the title allinanchor: searches the text links for the words
In very nontechnical language: allintitle returns those that have that keyword in title, allinanchor returns those that have that particular keyword in links pointing to that page.
Allinanchor: Websites/pages ranking depending on how many websites/pages (their number as well as importance) link to each of them with the searched anchor. Allintitle: Websites/pages ranking depending on what websites/pages have the searched word in their title, and how many times. Allinurl: Websites/pages ranking depending on what websites/pages have the EXACT searched word in their URL, and how many times. (the search function does not make any difference if the searched word is found in the domain name, or just in the file/folder name) Allintext: Websites/pages ranking depending on how many websites/pages have the EXACT (if you search with "") searched word in their content, and how many times. Good luck