Can someone clear up the difference between asking for time off compared to informing your employer of your absence?

I know this is anti work, but like or not, as long as it’s at will employment, the employers typically will have the say/power over the employees Hypothetically, say someone asks for a day off that’s a few weeks away and it gets denied for whatever reason. Then what? Options are accept it was denied, or not show up and deal with whatever consequence? I get that it’s supposed to be telling them of your absence, but what if a lot want the same days off? What would be the best way to tell your employer of your absense after it was denied? Do some people really quit over this?