卧底and 间谍 share the same meaning in English , but they are slightly different in Chinese. 卧底 usually refers to the police undercover, but 间谍, generally , implies the undercover working for the enemies or terror groups. E.G：他是警方派来的卧底，快杀了他！ 这人已经从事间谍活动很多年了，还是没有人知道他的真实身份。

这两个词可以互换，但更多的用法就是间谍一般是国家和国家之间的特工。 卧底一般用在警察派人安插在犯罪团伙里的人员。有时候互换来用问题也不大。 以上是我个人的理解和日常说法，可能不够严谨。

In general, these two words have the same meaning in Chinese context. But '间谍' sounds more official.

They have basically the same meaning.