Exactly. We have a confusion in terms.
Living here, I define a "local" place as a place with few or none haole patrons, where you walk in and they wonder why is this haole coming here? (translate into pidgin) If there were any tourists or even haoles I wouldn't call it local, and I wouldn't go in a local bar without some caution, especially as a single female.
"Local" cuisine generally involves large amounts of meat and fat, and some items that are delicious to most, some that are an acquired taste. I prefer the Asian cuisine myself.
Cinnamon roll place is not local style. Now locally owned small business that residents tend to patronize because they aren't jacked up and super tourist oriented, means something completely different.
Although I doubt there are that many little spots on Maui that aren't totally discovered by visitors. Not too many on the Big Island either.