If you are playing a show, do not lie. Get all of your paperwork and do it by the book. It's free and easy, especially if it's a DIY show with no guarantee. You just need the promoter to sign some stuff and follow a few simple rules. If they catch you in a lie, they can do all kinds of crazy shit that makes it hard or impossible to play or even visit in the future. You can email me if you'd like, chrislgrigg@gmail.com, I can try to track down the templates we used last time.
Yes, IIRC it has something to do with taxable money you may make from the gigs. So it's best to tell them you're visiting for leisure.