Can someone help me out with the relationship between Tathāgatagarbha and Buddha Nature. The way that Tathāgatagarbha was described to me was it's like someone finding an amazing jewel in a great heap of dung. I take this to be like the natural state of mind been very pure or radiant in some way. My understanding of Buddha Nature is similar. So are they related concepts? Do they come from different traditions or is my naive understanding way off?
They are the same thing. Tathagatagarbha is the most common Sanskrit term, but occasionally it is referred to with different terms like Sugatagarbha or Buddha-dhatu but they all mean the same thing.