There are many different types of Unicorn that live and breed in our world un-noticed.
The most commonly sighted is the white unicorn, the oldest and most dominant of Unicorns. Next is the black unicorn, which are usually cross breeds between a pegasus and a unicorn, which causes half-blood conflict between full blooded unicorns and pegasus. These species are usually outcasted.
The fire unicorn prefers to reside in the hotter rocky areas of the world, breeding by volcanos and hot springs.
The water unicorn live in deep forests surrounded by water, though they cannot breath under water they are excellent swimmers and prefer to eat the vegetation that grows in and around bodies of water.
To this day, the number of different species of Unicorn is unknown, and we are still discovering more and more over the years. Though these 4 are the only groups of Unicorns we've managed to observe.