public class UpdateDetailClass {

    public static void UpdateDetailMethod(List<Master__c> masterList) {

        Set<Id> masterIds = new Set<Id>();

        for(Master__c master : masterList) {
            masterIds.add(master.Id);
        }

        List<Detail__c> detailList = new List<Detail__c>([SELECT Id, Master__c, Master__r.isSelected__c, Type__c FROM Detail__c WHERE Master__c IN: masterIds]);

        List<Detail__c> detailToUpdate = new List<Detail__c>();

        for(Master__c master : masterList) {

            for(Detail__c d : detailList) {
                if(master.Id != null) {
                    if(master.isSelected__c == true) {
                        d.Master__c = master.Id;
                        d.Type__c = master.Type__c;
                        detailToUpdate.add(d);
                    }
                }
            }

        }

        update detailToUpdate;

    }

}

trigger updateTrigger on Master__c (after update) {
    if(Trigger.isAfter && Trigger.isUpdate) {
        UpdateDetailClass.UpdateDetailMethod(Trigger.New);
    }
}