How to export website field for a contact where website is specific website type?
I have a website type called Twitter Website, for storing Twitter "handles". Each website/handle contains 'twitter.com' (i.e., like www.twitter.com/joemcl ) 

So using Search -> Search Builder, I search for Contacts Website Like %twitter% , then select all search results, select Actions, then Add Contacts to a Group (or better perhaps, choose New Smart Group) to create a new Group of every contact who is a Twitter user. 

The same can work for Facebook as a website type. 

Obviously this won't work for type 'Work' or 'Home', which won't be in the website name, which is what I think you actually want.