In the
Star Trek universe (and others), "first contact" refers to the first (introductory) interaction between two
civilizations. In the movie "ST: First Contact" it is between the
Vulcans and
Humans.
Some "real" first contacts of note include Portuguese-Carib, Norse-Newfoundland natives, and Spanish-Inca. The track record is not good (the Norse didn't do too badly, but they still didn't get along at all). Maybe we needed a Prime Directive back then, alas it is too late now. I don't think any more true "first" contacts are possible until the day we meet some fellow travellers somewhere out there.
One can only pray that we are not treated with the same respect and sensitivity we have ourselves displayed.