What distinguishes 各位 (gèwèi) from 大家 (dàjiā)? From dict.cn:


各位 (gèwèi) = everybody
大家 (dàjiā) = everyone


So they seem closely related, but I don't think they're identical. Today is Teacher's Day and messages like "祝各位老师节日快乐" are popping up in my WeChat feed, and I don't think we can just swap 各位 with 大家 here without changing the meaning.

Question: What distinguishes 各位 (gèwèi) from 大家 (dàjiā)?
中文

“各位”和“大家”单独使用的时候基本没有区别。它们的主要区别在于“各位”可以接其他名词，而“大家”不能：


  各位家长、同学们
  大家家长、同学们  


同时，“各位”可以用于宾格，但“大家”听起来不太对：


  以后怎么做就要看在座的各位了
  以后怎么做就要看在座的大家了  


另外，在使用中，“各位”比较正式，常用于称呼及正式场合；而“大家”则显得比较随意，在日常中一般都使用“大家”。

还有一些习惯用法的不同：


  大家好！
  各位好！  




English

"各位" and "大家" make little difference when used alone. Their primary difference is that "各位" can precede other nouns, whereas "大家" can't:


  各位家长、同学们
  大家家长、同学们 (Wrong)  


Meanwhile, "各位" can be used as object, while "大家" sounds strange if used like that:


  以后怎么做就要看在座的各位了
  以后怎么做就要看在座的大家了  


Besides, in practice, "各位" tends to be a little formal and is often used in serious appellations and formal scenarios, while "大家" tends to be more casual and is more prevalent in daily spoken Chinese.

There's also some difference in usual practice:


  大家好！
  各位好！ (We don't really call people like this even in formal scenarios, even if it's grammatically correct.)