Search Engine Marketing works fundamentally differently, namely in its targeting.
Search Engines see that they have ~1,000 monthly hits for people searching for “Grilled cheese omaha” in Omaha, Nebraska. They allow you to run click-based ads to this audience based on live search volume — meaning, as people continue to search locally for Grilled cheese in Omaha, your sponsored ads will be presented at the top of search results (A.K.A., “the SERPs”), letting your customers know that you exist.
On a side note, the Geographic component (“Omaha”) appended to the “Grilled cheese” search classifies it as a Local Search — That’s 3 Pack & Local SEO territory. Know what that means? At the bare minimum, make sure your NAPs are consistent… If you’re interested in Local SEO you should check out our Comprehensive Guide to Local SEO on it.
So we’ve learned that Search Engine Marketing and Social Media Marketing are different in some fundamental ways, one of which is in their method for targeting. Neither method is necessarily better than the other, but prices and strategies will vary widely between them, and each is appropriate in a specific set of circumstances.