"A day off" is any day you are not working. "The weekend" means Saturday and Sunday. If Friday or Monday is also a day off for most of the people you know or work with, then it is a "three-day weekend" or "long weekend" or "Columbus Day weekend" or "Labor Day weekend."
Examples:
"We're going to see the fall foliage on Columbus Day weekend, would you like to come with us?"
"I'd love to, but I work at a mutual fund company, and we don't get Columbus Day off because the stock market is open that day."
"When I was a kid, Columbus Day was always celebrated on October 12th, but in 1971 they passed a law to move it to a designated Monday so that everybody could get a three-day weekend."
"May I take Wednesday as a day off? I have three personal days left this year."