Some folks once tried to explain by assigning "models" instead of types, calling the "Type I" a Model 1858 and the "Type II" a M1861 forage cap.
If photographic evidence is to be weighed, "Type I's" are seen to dominate through 1863ish, and the larger share of the Type II's fall thereafter.
Hat researcher and author Edgar Howell's studies of images showed that Type I's outnumber the Type II's overall by a 2:1 ratio.
This would seem to make some sense if the Federal supply system was initially heavily invested in the so-called M1858 (Type I) and then found the "war time" shift to the so-called
M1861 (Type II) slowly phasing them out. Plus the artifact pools tends to be slanted in favor of late War Type II's because of the greater survival rate of "late War" unissued/unused stuff.
PS... Oh, Phillips made BOTH Type I's and Type II's due to early War and late War contracts.
In gleichem Schritt und Tritt, Curt Schmidt
Not a real Civil War reenactor, I only portray one on boards and fora.
I do not portray a Civil War soldier, I merely interpret one.