个人认为有细微的区别.
be ata home强调在家里这个状态.而stay at home强调的是这个动作.一般人家会问你,Where is he?你说,He is at home.另外一种情况是人家问你What are you going to do in the summer?你回答说I prefer to stay at home.
不知道楼主能不能体会出着细小的区别.
仅是个人所见.口语中无论你说哪种别人都好明白只是各有各的侧重点.
老不明白,待在家里到底是“stay at home”还是“stay home”呢