The name Secret Service Special name was a trademark of the Fred Biffar Co., which was a mail order hardware company out of Chicago from the 1880s to about 1920. They were in the same type of business as Sears and Montgomery Ward.
This pistol was made by many different manufacturers. Here are a few pictures out of the Iver Johnson book of some of these pistols.
The Iver Johnson models
Hopkins and Allen model
The Meriden made version, which is the most common one found. The front sight is a dead give away of the Meriden model
H&R also made some of these pistols as did some Spanish companies. I have seen one of these pistols made by the Howard Arms Co. of Chicago, but it was actually made by Meriden.
These were very inexpensive pistols and not of the best quality. The H&R and Iver Johnson made models are of the better quality.