As in "we are going out tonight" using a different word for "we" depending on whether you mean "me and some other people" or "you and me (and potentially other people as well)".
Yes, this feature is called clusivity, there are dozens of languages that have it, for example Mandarin Chinese, Vietnamese, Malay, Hawaiian, etc. This article has a list of such languages together with their inclusive and exclusive forms of "we": Clusivity (Wikipedia).
This is called clusivity, and although not found in European languages (AFAIK), it is found in South Asia and Australasia at least.
An example of how this is used (as taken from Fantastic Features We Don't Have In The English Language (YouTube)):
We've just won the lottery!
In English this is unclear - is the listener included? If English had an exclusive/inclusive 'we', then it would be clear if the listener was also one of the winner.
I haven't got enough reputation to comment, but I must add this link because WALS is such an amazing tool for these type of questions:
This will show the answer to your question on a map. Explore other features by clicking Features in the menu.
In Vietnamese there are 2 types of "we":
inclusive we: "chúng ta", to address the speaker, the person spoken to, and maybe others if any
exclusive we: "chúng tôi", to address the speaker and others, excluding the person spoken to.
This was asked here: Is there a language which distinguishes between three types of "we"? (1) speaker and person spoken to (2) speaker and others, excluding person spoken to (3) speaker and others, including person spoken to?
Norwegian Sign Language distinguishes between inclusive and exclusive "we". Apart from that it distinguishes between dual and plural, so there are different signs for:
- we (2 people, listener excluded)
- we (2 people, listener included)
- we (more than 2 people, listener excluded)
- we (more than 2 people, listener included)
I don't know about other sign languages, but I wouldn't be surprised if this kind of distinction was common among them.