I believe in both. Unicorns are mentioned multiple times throughout the Bible (9 to be exact). Thus, they are real.
Here are a few.
Deuteronomy 33:17: His glory is like the firstling of his bullock, and his horns are like the horns of unicorns: with them he shall push the people together to the ends of the earth: and they are the ten thousands of Ephraim, and they are the thousands of Manasseh.