Depending on the region, both terms can synonymous and normally refer to official holidays; the days when people don't work in a country or a region.
But there are some nuances: Sometimes, the word "feriado" means a day when an institution's employees don't work, even if it's not an official holiday. For example, although the law says people should work on Mothers' Day in Mexico (it's May 10th), many companies and schools don't work, so they say it's a "día feriado" for them. Also, despite the fact that one should be working, it's still called a "día festivo", because it's a celebration day.
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