In my county, it varies from department to department (My sandbox syndrome).
If it is called into county, with a report from the alarm co, that someone on site with passcode states no fire, set of by burnt food, requests no response... some Co's still send a fire response, some just let a Chief officer know, and they usually drive by and check.
If it is called in as "alarm sounding" by a real person, or a Waterflow/fire alarm by an Alarm Co.... with no reports of any fire/smoke condition, it is dispatched as an Automatic Alarm.... the response here varies.... during the day, some companies will call for almost a full box assignment (several engines, ladders, etc), because that way, usually at least 1 engine will get out from 1 of 3 companies.
My company sends 1st engine at emergency speed, 2nd at reduced rate, to stage at hydrant, and AT LEAST one chief, running hot "Rushing to Recall" - to beat the engine in so they can cancel the Co..... stupid.... just go to station and help get the truck on the street.
As soon as there is a report of a smoke condition, or sometimes even an odor..., it gets upgraded to a full "dwelling / building" response.
Also, some places will send more apparatus on a "high hazard" box.... the High School, or a Nursing Home, for an Alarm might get an extra engine or 2, and maybe a ladder, just becaue it is a large building with greater threat to life....
Jon