Michael:
The General - Single Field style is designed to be used to search for unique names or string values such as census tracts, parcel id numbers, place names, meter numbers to name a few. The type of search that is performed is an exact look up of what is in the reference data for the mapped Single Key field. General - Single Field style
The General - Gazetteer style uses search logic that will take into account spelling instead of an exact search, so if the reference data has "Carmel by the sea" in Californi as the city or place name, you could search for 'Carmel' California and get a match or candidates returned, whereas the Single Field locator would be expecting an exact input of "Carmel by the sea". The Gazetteer style can be used to search for the same unique features that you would use the Single Field locator, but it handles suggestions better than Single Field. General - Gazetteer style
Have you tried the Gazetteer style yet with suggestions in your application/workflow?
Are you using the Single Field style to search for addresses? It's not recommended style to use for searching for addresses if your reference data is point or polygon geometry. The US Address - Single House style is the style that should be used when you have point or polygon (parcels, tax lots) geometry that you want to use as the reference data for the locator.
-Shana