1、侧重点不同
remain 强调“继续停留于一处或保持原状态、情况性质而不改变”。
例句：Train fares are likely to remain unchanged.
火车票价很可能会保持不变。
The date and venue of the game must remain under wraps
比赛的时间和地点必须保密。
remain silent/standing/seated/motionless
依然沉默 / 站着 / 坐着 / 一动不动
Much remains to be done.
还有很多事要去做。
They remained in Mexico until June.
他们在墨西哥一直住到六月。
The three men remained silent
这3个人保持着沉默。
He will have to remain in hospital for at least 10 days
他至少得在医院里呆10天。
The situation remains tense
形势持续紧张。
We must not shrink from the legitimate use of force if we are to remain credible
我们要想保持诚信可靠，就绝不能避忌武力的合法使用。
《柯林斯高阶英汉双解学习词典》
stay强调“某人[物]继续留在原地而不离开”。
例句：Can you stay behind after the others have gone and help me clear up?
你能不能等别人走后留下来帮我收拾收拾？
2、延伸意不同
stay还可表示”暂住、短期停留”:
例句：‘Do you want a drink?’ ‘No, thanks, I can't stay.’
“你要不要喝一杯？”“不，谢谢，我不能久待。”
They stayed talking until well into the night.
他们待在那儿一直谈到深夜。
He is staying at Hilton Hotel. 他住在希尔顿饭店。
Gordon stayed at The Park Hotel, Milan
戈登下榻在米兰的帕克饭店。
He stayed to see the end of the game. 他一直呆到比赛结束。
My mother-in-law stayed with us this week when she visited us.
我岳母本周来看望我们时，一直和我们在一起。
I stayed three nights at my cousin's house.
我在我表兄家住了三夜。
My sister's coming to stay next week.
下星期我妹妹要来住几天。
Could I stay tonight?
我今晚可以留下吗？
《柯林斯高阶英汉双解学习词典》
remain还可表示“继续保持或处于原来的状态”。
例句：In spite of their quarrel, they remain the best of friends.
尽管有过争吵，他们仍是最好的朋友。
This place remains cool all summer. 这个地方整个夏天都凉爽。
Schools and government offices have been closed, and many shops remain shuttered.
学校和政府办公楼都关闭了，许多商店的百叶窗也一直关着。
另外，表示“遗留，残留、剩下”时，只能用不及物动词remain，例如：
This visit will always remain in my memory.
这次访问将永远留在我的记忆中。
It will remain an indelible stain on his memory.
这将成为他记忆中一个不可磨灭的污点。
《汉英大词典》
The scene will remain forever engraved on my memory.
那情景将永远铭刻在我的记忆中。
Not much of the house remained after the fire.大火过后，房子里没剩下多少东西了。
Of the seven brothers, only four now remain; the rest are dead.
七兄弟中，只剩下四个，其余的都死了。
3、也有共同点
表示“继续呆在某处”或“保持继续”时，可用不及物动词remain或stay，例如：
He remained in his seat after all the other students had gone home.
其他学生都回家后，他仍坐在座位上。
From time to time, James remained at home with his family.
詹姆斯偶尔留在家里陪家人。《柯林斯高阶英汉双解学习词典》
In the old days the woman stayed at home and the man earned the money.
过去，女主内，男主外。
《柯林斯高阶英汉双解学习词典》
表示“继续保持或处于原来的状态”时，可用remain或stay，例如：
Three of them remained single. 其中三人仍然单身。
Shops should remain open till later in the evening. 商店应该一直营业到晚上晚些时候。
The store stays open until late on Thursdays.
这商店每星期四都会开到很晚。
Inflation stayed below 4% last month.
上月的通货膨胀率保持在4%以下。
The fact remains that inflation is unacceptably high
事实是通货膨胀率仍高得离谱。
《柯林斯高阶英汉双解学习词典》
The door stayed closed.But the police themselves prefer to stay unarmed.门一直关着，但警察自己却宁愿手无寸铁。
那么现在抗击新冠提倡待在家里就是：
stay in
不外出；待在室内
to not go out or to remain indoors
I feel like staying in tonight.
今晚我想待在家里。
stay on
留下来继续（学习、工作等）
stay out
1
待在户外；不在家；（晚上）不回家 ； 继续罢工
stay up
深夜不睡；熬夜
You've got school tomorrow. I don't want you staying up late .
你明天要上学。我不想让你熬夜。
