The first bullet, which has a conical base-cavity and no body-rings, is a Confederate-made .577-caliber Enfield "Minie-Ball." The British-made version of it (which was imported and used in large quantities by both sides in the civil war) always had a "plug-shaped" (flat-bottomed) cavity in its base.
The second bullet is one of the many-many varieties of .44-caliber bullets. Some were rifle bullets and some were for pistols. To give you its correct ID, we need several more side-view and base-view photos of it.