What it appears you have there is either a Grade 0E, or 1E. On guns of this era, the grade stamp is often on the barrel flats near the lug, which is not included in one of your photos. Both grades featured a small amount of line engraving, although the Grade 1 typically had a small flourish of scroll; but your is very early and early guns have a lot of inconsistency. Catalogs listed Twist barrels as standard for the Grade 0 gun up to 1898, and Damascus barrels for the Grade 1. In 1900, the Grade OE carried a retail price of $60, and the Grade 1E a retail price of $75.
Not having seen the release on your Pigeon, I can't explain to you the difference, but the release on this gun is the standard "banjo-style" roll-releae used on Smith ejector guns from this era and having the 1901 patent date (the "banjo" style escutcheon is actually the second style roll-release escutcheon used for Smith guns with the 1901 ejector patent, the first style was round with two exposed mounting screws).
According to the serial number records from this era, which have a lot of holes, your gun would have shipped sometime between 1891 and 1898. Now this fact begs other questions, the first being why does this piece have the second type ejectors (1901 patent) on such an early gun? The answer, since the gun frame lacks the frame cuts peculiar to the early roll-type joint check normally seen on Smith guns within this serial number range, is that this frame languished in inventory for several years before an order was received for this particular lower-grade ejector gun (I have a copy of an 1895 shipping ledger page for 52 ejector guns, mostly Grade 1s, and some of those frames were in inventory for more than 3 years prior to receipt of an order; at which time the gun was placed into production and ultimately shipped). The second answer is that the gun was returned at a later date and factory retro-fitted with ejectors.
As to your barrels, I am not an expert in Damascus but have not seen that particular pattern on another Smith gun from any era. In his book on Remington shotguns, Charles Semmer shows samples of various damascus barrel patterns and two such patterns noted in his book closely resemble the pattern on your barrels; one is marked "chine P" and the other is marked "ohonon 6.S.T." Those barrels are striking, and why Hunter used these non-standard tubes on this gun will forever remain unknown (a special order maybe; or perhaps an odd set getting "stale" in inventory?); but low grade Smith guns with ejectors are not very common, so I hope you have this gun properly restored at some point. As FYI, a Silver's rubber pad would be period correct for your gun.
