Bud Jones chips are not made of clay, but you already know that. However, they are not made the same way as clay chips, either. Based on what I've heard about the classic Bud Jones manufacturing process, here's what happens. I can't swear that this is current, since my info is a few years old.
BJs are injection molded in several steps, depending on the colors and patterns. But then they are finished on a high-speed machine that shapes them so each chip is identical, cutting off excess material. The finishing process includes rounding or beveling the edges, plus creating a very smooth and level face.
So no, BJs do not come out of a mold with sharp corners, like Paulson clay chips. Depending on how they were ordered, they come with a beveled or rounded edge, with a varying amount cut off depending on the specs. I have BJs with nearly square edges, and a few that have an intricate beveling pattern. The better V7 chips tend to have fancier rounded or beveled edges.
B&Gs (and Matsuis, I think) are made by a newer process that does not include the machining at the end.
Look at the fine rounded edge on this chip:
And you should be able to make out the different edges on some of these chips:
