The two ways that both Buddha Nature and soul are actually similar is in the concept of being both “natural” and “luminous.” Where they absolutely differ is on the concept of ego and self; soul implies permanent attachment to a “self” which, at its core, is the opposite of the Buddhist ideal of Emptiness.
Also, in most traditions, happiness of the soul rely on the blessings of God. In Buddhism, you could say it is completely self-help — only you can develop your Buddha Nature. (People, Yidams, Buddhas can help, but ultimately you have to do it.)
If it is not the soul, what is Buddha Nature?
Buddha Nature is a lofty concept, understood by Enlightened Beings, but in a certain way unteachable to the unenlightened. In the Uttaratantra it says:
“It is subtle, so it is not the object of learning.
It is ultimate, so it is not the object of contemplation.
The dharmata is profound, so it is not the object of mundane meditation…”
Realizing it is there, as taught by infallible Buddhas, is uplifting and wonderful. Understanding exactly what it is more difficult. It can be discussed, to a certain extent taught or commented upon, but ultimately it is “ultimate” wisdom, far beyond our current ability to fully grasp. On that level, it requires faith. But, for those who accept the infallible teachings of Buddha, it is not faith, but acceptance of truth we don’t yet fully understand. Even though we can’t fully understand, it is important to know we have Buddha Nature.