Its always called an eagle but I've always thought it looked more like a dragon, or perhaps a phoenix. The change from red to black was in mourning for the passing of Sturm, and his name was kept as part of the official company name.
SIG is a bit unique, Schweiterische Industrie Gesellshaft, which translates to Swiss Industrial Company or roughly "Swiss Industry inc"
For many, many years Swiss law prohibited SIG firearms from being sold outside Switzerland. SIG entered into a partnership with J.P. Sauer & Sohn, an old established German gun maker, to make SIG designs in Germany, and market them to the world, under the name SIG-Sauer.
One of my favorite pistols is my Browning BDA 45 (circa 1980) which is the original SIG P220 design. The gun is marked Browning on one side of the slide and SIG-Sauer System made in W. Germany on the other.
I'm not sure, but I think the only gun Ruger was making before Sturm passed was their .22 semi auto pistol and red eagle .22s are sought after collectors items.