Remington No 1 Creedmoor

[Caprock]

According to Roy Marcot's Book on Remington Rolling Block Rifles, Page 155,

44 S (S means special) typically chamber the .44-77 (2 1/4 inch bottleneck case) and the 44-90 (2 1/4 inch bottleneck case.)

Rifles stamped 44 CTG'E S take the same ammunition as above and was seen on the earliest Creedmoor Target Rifles.

Rifles Stamped 44 S 100 typically chamber the 44-100 Remington Special Cartridge bottleneck loaded with 100 grains of powder and the shoulder is further forward than on the 44 S (44 2 1/4" case)

Only a very few #1 Creedmoor Rifles were chambered for the 44 2.4 or 2.6 straight case as those were introduced in 1880 for the Hepburn

I think if you'll check 44S could also be the 44-90 2 7/16 BN