Except for a small difference in the inside muzzle ring diameter and the manner in which they are serial numbered, both bayonet types appear to be almost identical. Both have Collins Type 2 short hilts and an unusual guide slot length of ~20.0 millimeters.
What makes them different
First, the Sharps Model 1859 has a muzzle ring diameter of ~20.8 millimeters and the Spencer Navy has a muzzle ring diameter of ~ 20.2. Not a big difference but enough to make interchangeable issues. So not for the same rifle.
Second, is the manner in which the bayonets are numbered to the rifle.
The Sharps serial number is a small font five digit number in the 40000 to 45000 range and it is usually stamped horizontally near the center of the hilt flat. It is a very distinctive marking and easy to identify.
Sharps Model 1859
The Spencer serial number is a two to three digit number usually stamped on the end of the pommel but has been seen on the side of the pommel and the center of the crossguard. The font is typically larger than the font used on the Sharps bayonets.
Spencer Navy
Speculation and questions