To me a  "gig" is a job,  which means you get paid.  You could participate in a  "jam" at a club or friend's house.  You could go to a  "hootenanny"  around a campfire.  You can  "woodshed" at home,  or  "play" a benefit.  A gig is special.  You're expected to set that date aside in your calender,  show up and put on a professional musical entertainment,  for hours specified,  and expect payment in return.  If anouther musician tells me that  "we've" got a gig and wants me to participate,  that's what I expect.  If you want to call any of these examples a  "gig",  feel free,  just don't change your terminology to your musical mates at the end of the evening in question.  "Oh,  when I said a  "gig" I meant......."