Shirogami 1 (White 1) has a higher carbon content than Shirogami 2 (White 2), roughly 1.3% vs 1.1%, making it the purer carbon steel and the one some craftsmen still regard as the best, though in practice the two have become harder to distinguish as modern metallurgy has made both quite pure.

White 2 (Shirogami #2) has about 1.1% carbon and a hardness range of 60-64 HRC; White 1 sits around 1.3% carbon. That 0.2% difference is the core spec gap. More carbon generally means you can push hardness higher and hold a keener edge, but it also makes the steel more brittle and less forgiving. White 2 trades a bit of that potential peak sharpness for slightly better toughness and ease of sharpening.

Shirogami 1 carries a certain prestige. Sukenari's Nobuo Hanaki once told me directly that they only use White 1 for their mizu-honyaki because it is the pure form of carbon steel, it carries that halo. Among traditional smiths, White 1 is still spoken of as the benchmark. That said, in recent years the improvement in metallurgical manufacturing has narrowed the real-world gap. The rumor is that both grades are now so pure that separating them in practice is no longer straightforward. I've also heard that Hitachi has stopped producing White 1, though I can't confirm that.