没有区别，正如在javadoc中声明的那样:

public boolean add(E e) {
    return offer(e);
}

从队列API:

offer方法尽可能插入一个元素，否则返回false。这与合集不同。方法，该方法只能通过抛出未经检查的异常来添加元素。offer方法设计用于故障是正常情况，而不是异常情况，例如在固定容量(或“有界”)队列中。

没有区别，正如在javadoc中声明的那样:

public boolean add(E e) {
    return offer(e);
}

Priority Queue has some priority assigned to each element, The element with Highest priority appears at the Top Of Queue. Now, It depends on you how you want priority assigned to each of the elements. If you don't, the Java will do it the default way. The element with the least value is assigned the highest priority and thus is removed from the queue first. If there are several elements with the same highest priority, the tie is broken arbitrarily. You can also specify an ordering using Comparator in the constructor PriorityQueue(initialCapacity, comparator)

示例代码:

PriorityQueue<String> queue1 = new PriorityQueue<>();
queue1.offer("Oklahoma");
queue1.offer("Indiana");
queue1.offer("Georgia");
queue1.offer("Texas");
System.out.println("Priority queue using Comparable:");
while (queue1.size() > 0) {
    System.out.print(queue1.remove() + " ");
}
PriorityQueue<String> queue2 = new PriorityQueue(4, Collections.reverseOrder());
queue2.offer("Oklahoma");
queue2.offer("Indiana");
queue2.offer("Georgia");
queue2.offer("Texas");
System.out.println("\nPriority queue using Comparator:");
while (queue2.size() > 0) {
    System.out.print(queue2.remove() + " ");
}

输出:

Priority queue using Comparable:
Georgia Indiana Oklahoma Texas 
Priority queue using Comparator:
Texas Oklahoma Indiana Georgia 

除此之外，你还可以定义Custom Comparator:

import java.util.Comparator;

public class StringLengthComparator implements Comparator<String>
{
    @Override
    public int compare(String x, String y)
    {
        //Your Own Logic
    }
}

作为使用Comparator的替代方法，您还可以让您在PriorityQueue中使用的类实现Comparable(并相应地重写compareTo方法)。

注意，如果排序是对象的直观排序，那么通常最好只使用Comparable而不是Comparator——例如，如果您有一个用例要按年龄对Person对象排序，那么可能最好只使用Comparator。

import java.lang.Comparable;
import java.util.PriorityQueue;

class Test
{
    public static void main(String[] args)
    {
        PriorityQueue<MyClass> queue = new PriorityQueue<MyClass>();
        queue.add(new MyClass(2, "short"));
        queue.add(new MyClass(2, "very long indeed"));
        queue.add(new MyClass(1, "medium"));
        queue.add(new MyClass(1, "very long indeed"));
        queue.add(new MyClass(2, "medium"));
        queue.add(new MyClass(1, "short"));
        while (queue.size() != 0)
            System.out.println(queue.remove());
    }
}

class MyClass implements Comparable<MyClass>
{
    int sortFirst;
    String sortByLength;

    public MyClass(int sortFirst, String sortByLength)
    {
        this.sortFirst = sortFirst;
        this.sortByLength = sortByLength;
    }

    @Override
    public int compareTo(MyClass other)
    {
        if (sortFirst != other.sortFirst)
            return Integer.compare(sortFirst, other.sortFirst);
        else
            return Integer.compare(sortByLength.length(), other.sortByLength.length());
    }

    public String toString()
    {
        return sortFirst + ", " + sortByLength;
    }
}

输出:

1, short
1, medium
1, very long indeed
2, short
2, medium
2, very long indeed

在这里，我们可以定义用户定义的比较器:

以下代码:

 import java.util.*;
 import java.util.Collections;
 import java.util.Comparator; 


 class Checker implements Comparator<String>
 {
    public int compare(String str1, String str2)
    {
        if (str1.length() < str2.length()) return -1;
        else                               return 1;
    }
 }


class Main
{  
   public static void main(String args[])
    {  
      PriorityQueue<String> queue=new PriorityQueue<String>(5, new Checker());  
      queue.add("india");  
      queue.add("bangladesh");  
      queue.add("pakistan");  
 
      while (queue.size() != 0)
      {
         System.out.printf("%s\n",queue.remove());
      }
   }  
}  

输出: 印度 巴基斯坦 孟加拉国

提供和添加方法的区别:链接