Except for minor details in the texture and finish of the brass hilts and markings, both bayonet types appear to be almost identical. Both have Collins Type 1 long hilts and a guide slot length of ~12.4 millimeters. The muzzle ring diameters and lug slot dimensions are basicly the same and they should be interchangeable to the rifle.
What makes them different
First, the hilt ribs on the Remington Model 1862 bayonet have a rough grainy texture. whereas, the Unknown Collins bayonet has a smooth polished texture.
Remington Model 1862
Unknown Collins
Second, the muzzle ring walls of the Remington M1862 are noticeably thicker than the Unknown Collins. The inside muzzle ring diameter is ~22.8 millimeters on both bayonets. The outide diameter of the muzzle ring is ~32 millimeters on the Remington M1862 and ~29 millimeters on the Unknown Collins.
Remington Model 1862
Unknown Collins
Third, the hilt of the Remington M1862 is slightly wider and heavier than the Unknown Collins hilt. Some of the Remington M1862 hilt flats have not been polished after casting.
Remington Model 1862
Unknown Collins
Finally, the markings are different.
The Remington M1862 is typically stamped B.H. on the hilt flat immedately behind the muzzle ring. It also has small single digit alpha characters stamped on both sides of the cross guard and on the left ricasso.
Remington Model 1862
The Unknown Collins is typically stamped on the hilt flat with a two or three digit number in a fairly large font. Most observed examples have a Collins Logo #1 on the left ricasso and dated 1861 on the right. Examples of the Unknown Collins have been observed without the logo and date markings.
Unknown Collins
Speculation and questions
Obviously, the hilts were cast from different molds but could they have been made for the same rifle?
Could we be looking at a difference between early production versus later production of Remington Model 1862 Rifle bayonets? The numbers found on the hilt flat of the Unknown Collins bayonet are probably mating numbers to a rifle they were adjusted to fit. The observed numbers have been small, three digits or less. Somewhere around 10,000 of the rifles were produced. Did Collins produce the first few hundred bayonets then pass production to Remington?
Most references claim that E. Remington & Sons made the Remington Model 1862 bayonets but almost every aspect of this bayonet appears to have been made by Collins & Company. Maybe Collins started production of the bayonets, marking them in their standard manner. Then production was passed to Remington who copied Collins construction in minute detail. Maybe Remington assembled the bayonets from parts supplied by Collins? Maybe Remington just sent inspectors to Collins' factory to inspect and approve the production process.
All of this is pure speculation on my part.
The purpose of the Unknown Collins bayonet still remains a mystery.