In the US, a "holiday" is day like Christmas, Thanksgiving or Labor Day and we take a "vacation" from work where we might travel somewhere. In the UK, the word "holiday" serves both these functions. That said, the first example you give isn't really standard English on either side of the Atlantic. "Holidays" usually means the season near the end of the year that includes Christmas and New Year's Eve and New Year's Day, but it can also mean all of the holidays throughout the year. But in the Romance languages, the equivalent of "vacation" is always used in the plural. Your first example may just be a direct translation gone bad.