Yes, 8x57 came first. The original version of the cartridge, the Patrone 88/8x57I (the I stood for Infantry), appeared in 1888. The final version with .323" diameter bullets, the "S" diameter, appeared in 1905, when the bullet was also changed from a 225-grain roundnose to a 154-grain spitzer. The chamber throat was also shortened to better accommodate the lighter, sleeker bullet. (The next year the U.S. military changed the standard 1903 Springfield's load from a roundnose 220-grain to a 150-grain spitzer. The chamber throat was also similarly shortened.)
However, some commercial 8x57s retained the .318 bullet/groove diameter after 1905, notably break-action guns chambered for the 8x57 rimmed.
