The M1860 had a long service life from 1860 until it was replaced by the M1902 all-officer's sword. In addition to US Army and various State militia elements, it was used extensively by veterans' and fraternal groups, military schools, etc, often well into the 20th century. There were a number of pattern changes make over time. The original had an undecorated folding rear counterguard and a gilt brass mounted blued or browned scabbard with two carrying rings.
Later scabbards changed to a nickel plated scabbard with three carrying rings like this one.
In 1872 a major change was made to the design by addimg a rather elaborate design to the rear folding counterguard.
In 1878 Springfield Arsenal made another major change to the swords it produced, the main difference being that the rear counterguard was cast in fixed position. Private manufacturers did not commonly follow this second change. Most either continued to use a folding rear counterguard or, on cheaper examples, eleminated it.
All the M1860 variants which were used by the Army had a fixed front counterguard with an eagle backed by a panoply of flags. There was a lot of variation of detail, e.g. a federal shield on the eagles chest or not, a wreath around the eagle or not, etc.
M1860 swords used by non-Army groups often had a different front counterguard design. Most commonly encountered of these are GAR swords which featured fancy interlocking GAR initials.
It appears your second sword does not have a rear counterguard. I would guess, based on this and other design features, that your sword is a non-Army sword from the late-1800s. I really can't make out from the picture what design is on your front counterguard - I don't see a pelican. This design would probably provide the best clue as to the original user of the sword. It also seems your sword blade may be etched. If so, this could also provide a clue to the original group.