I think everyone is confused on S&W model numbers (maybe even S&W), but the gun being described is the "Bodyguard", which was originally the Model 38 (Airweight) and 49 (Steel). There have been several variations since. It is both double and single action. The Centennial (Model x40 and x42) has a fully concealed hammer and can be fired only double action.
The Bodyguard has a partially concealed hammer and that "slider thingy" is the hammer spur, which protrudes just enough to allow the hammer to be cocked with the thumb. It is a good compromise for people who want a snag-proof revolver for concealed carry but who also want single action capability. So the Bodyguard is in fact single and double action, just like most other S&W revolvers, even though only the top of the hammer is visible.
Jim