Are you asking about the J. Stevens Arms & Tool Co. singles, or the post-1916 J. Stevens Arms Co., Chicopee Falls singles, or the post-1920 purchase by Savage Arm Co. singles?
Have you seen this?
U.S. Single Barrel Shotgun Identification | Shotgun Forum (shotgunworld.com)

 

This thread is massively helpful, but I must not be adept enough to identify the shotguns I have.

If you have expertise that you would be willing to share, I would like to ask you to help me ID these two shotguns. What I'll do is to include information about them in two separate replies to your post.

The first is only stamped on the left side of the receiver "J. Stevens Arms & Tool Co. // Chicopee Falls Mass. U.S.A."

On the top of the barrel is "ELECTROSTEEL*CHOKEBORED", there are no other stampings visible on the outside of the gun

underneath in various places, i.e. the underside of the barrel, on the fore end locking piece, on the wood of the fore end, and in the opening of the receiver, is stamped "BY 432". All of these stamps are very well impressed into the metal, it looks to me like they weren't making it in haste.

Certain models in your post were labelled "ejector models," but in my understanding, ejection is a different step of the process from extraction, I will include pictures, but is the part that does the extraction what they call an "ejector" in their advertisements? The break action works by means of a checkered lever behind the exposed hammer and the trigger guard is detachable via unscrewing it.

Just about all the finish is worn off, but after a thorough inspection, it was color case-hardened when new.

 

No. 100, 110, 105, 107, 115 & 125 singles were listed with "Electro Steel"
Your gun is a pre-1916 No. 105 if the extractor simply lifts the shell from the chamber, or a No. 107 if it ejects the shells after firing

 

The second one - with the broken firing pin - is most likely a post Savage acquisition, and although the gun more or less has the same features, the stock profile is simpler and the stamped markings are clearly done in haste and without precision, I am curious what nomenclature changes were made post acquisition.

On the left of the receiver is "J. STEVENS ARMS COMPANY // CHICOPEE FALLS MASS. U.S.A.", and on the right, there are two stampings: one is what looks like a "T" with a circle around it, and the other says "TRADE[MARK] // STEVENS // REG. U.S. PAT. OFF. & FGN."

The barrel has only one visible stamping, "PATENTED AUGUST 12.1913"

It was finished much the same way, but the wood, either by the factory, or my friend's grandpa, put a coat of lacquer on it.

The firing pin from the older gun looks the same as the fragments of the one in this newer gun.

Another thing, this newer gun has an aluminum bead sight, but the older gun is missing its bead sight. As someone more knowledgeable on these old single shots, which would be more correct as a replacement, brass or aluminum? I have inclinations, but your level of knowledge on these guns is making me catch the single shot collecting fever.

 

Older guns had brass; newer guns had aluminum. I don't know when the change occurred.