According to the UoF Extension article, Bok Choy and Pak Choi are exactly the same thing.
No mater what you call them though, they are absolutely delicious, one of my favorite vegetables, and definitely at their best when grown in fall and early winter. Michihli cabbage is also a favorite, and growing it is about the only way to get it. In the mild winters along the West Coast it grows extremely well in late fall and holds in the garden right through winter - I pick individual stalks off the outside of the plant, just like celery. It seems less susceptible to slug damage and rot than the heading types. Stir-fries in February are the best!