The google autocomplete and search suggestions is actually drawing from a database of previously asked queries.
Then, it looks like they're using some sort of AJAX or similar script to hit recent queries as you're typing and give you suggestions.
However, Smith Cart *does* have the ability to use additional search terms and phrases. While it is not "interactive" like Google's auto-complete, it does allow you to "flesh out" common spelling mistakes and common phrases.
For example, we have products that say "Skate", "Skating", and so forth. But also in the additional search fields I may put "Skateing", even though it is mis-spelled, for people who mis-spell it. Additionally, since they search for "skate", they might miss products that say "Skating" in the description, so I make sure that those are fleshed out as well.
So, for a couple of products, say "Blue Skates" and "Dog Rollerskating", my search terms may say things like "skate", "skating", "skateing", "rollerblades", "rollerskating", "roller skating" and so forth so that the user gets "best guesses" for the products.