The bullets for each are the same size. 30 caliber or 0.308" The cases are the same length but the 300 wsm is much fatter. Reloading is very different. As a general rule you will use slower powders and much more of it for the 300 wsm.
yes, bullets will work in both calibers, but depending what you are using them for, you might want to think about other grain bullets. I try to stick with 165/168 gr bullets in my 308 and 180's in my wsm, for deer hunting. I have had 165's in my wsm, on a close deer shot, come apart and not penetrate completely. 308 is a large rifle primer and wsm is a large rifle magnum primer. jim