A Youkai is an animal/creature, and at times even an inanimate object, that's training to become a Sennin. Youkai have a different transition than Doushi do to becoming Sennins, and it differs depending on the type of Youkai.
Most Youkai start as creatures, or in some cases like Ou Kijin's, they may start as an inanimate object (i.e. a stone lute). After bathing in the sun and moon's light for a thousand years, they become a Youkai Sennin.
In some cases, like Youzen's, they may be born naturally as Youkai.