I have a scenario where i want to update the lead record's rating field when the status changes to status == 'Closed - Not Converted'.And i wrote after update trigger  for this: Below is the code

trigger leadUpdate on Lead (after update) {
list<lead> leadUpdate = new List<Lead>();
    for(Lead l :trigger.new){
        if(trigger.oldMap.get(l.id).status != l.status && l.status == 'Closed - Not Converted'){
           lead ld = new lead(id = l.id,rating = 'cold');
            leadUpdate.add(ld); 
        }
    
    }
    update leadUpdate; 
}


And samething can be achieved through  before trigger as well. Below code:
trigger  leadUpdate on Lead (before update) {
List<lead> leadUpdate = new List<Lead>();
if(trigger.isBefore && trigger.isUpdate){
         for(Lead l :trigger.new){
        if(trigger.oldMap.get(l.id).status != l.status && l.status == 'Closed - Not Converted'){
           l.rating = 'cold';
            leadUpdate.add(l); 
        }
    
    }
   
    }
}

I want to ask which one is the correct approach and what is the difference?