Under the hood contains uses LIKE, search uses the full-text search capabilities of the database.
https://stackoverflow.com/questions/224714/what-is-full-text-search-vs-like
Full-Text Search also does stemming, given "Quick brown fox"
contains: "foxes" will return nothing
search: "foxes" will return the result
Also if you add indexes, full text search can be quite a bit faster for querying.