I’m not sure I’m seeing the distinction you’re suggesting between the two categories of unicorns, especially given the examples.
Take Google for example. Plenty of search engines existed before Google and they in-fact worked exactly the same way: put in a keyword and get a list of results. Google simply improved upon the algorithm to make the results much better. So maybe this falls in the second category?
Or Facebook: MySpace and Friendster both existed before Facebook did. Facebook brought real identity, news feed, like button, etc. but social networks were already there.