An emergency mobile mechanic is the same local mechanic with a different queue. Scheduled maintenance waits; the car that's stranded in a driveway at 7 a.m. before a shift, the one that overheated on the way to daycare pickup, the one whose brakes went soft on the highway, those go first. That's how our mechanics in 250 cities run their day.
Emergency doesn't mean rushed. The diagnosis still comes before the repair and the quote still comes before the work. It means the mechanic reorganizes the schedule to get to you fast, loads the likely parts before leaving and aims to finish the job in one visit so you can get on with your day.
If your car can't move or isn't safe to drive, reach out through your city page on Mobile-Car-Repair.xyz and say it's urgent. The mobile mechanic will tell you honestly how fast they can be there.