The long staff is a Jhoong Bong (While this is just a standard broom handle, it's only a little shorter than Jhoon Bong, and suffices for practice away from the school. This is also quite a bit lighter than the Jhon Bongs at school.)
Early Tai Chi form: Tai Gup Chung
Linear form is Pal Baek Gae.
(Note: This post will be updated periodically as I learn more of these.)