From what I've read over the years, the "rebound slide" - the square bar of steel that sits behind the trigger and under the hammer - is the original hammer drop safety and has been part of the S&W double action design from its inception in the late 19th century. Its purpose was to allow carrying the revolver with all chambers loaded with no risk that it would go off if dropped in a way that the hammer got hit - an advertising plus over the Colt Single Action which required an empty chamber under the hammer to be drop safe.
As for the second, sliding bar safety found on exposed hammer guns, the story I've seen is that during WWII some sailor dropped a S&W revolver which hit the deck in a way that smacked the hammer, which was at rest, not cocked. But the impact broke off the little nose at the bottom of the hammer which rested on the rebound slide, and normally kept the firing pin away from a primer. The broken hammer was then free to continue forward and fire the round in the chamber, killing the sailor.
To prevent this type of accident, the second hammer block was added. Like the rebound slide, it is moved out of its blocking position by the rearward movement of the trigger, and moves back into blocking position shortly after the trigger starts to move forward from its rearmost position. But the rebound slide moves forward as well. Either, and both, will block the firing pin from reaching a primer if the hammer moves forward without the trigger being held fully back.
Neither of these hammer blocks is related to whether the revolver is cocked in single action or not. The second, newer block was simply added to address a specific hazard which revealed itself after about 50 years of use of the original design. But since the hazard was limited to guns with exposed hammers (that might be struck hard enough to break the hammer and thus bypass the original, rebound slide block) there was no need to add the second blocking device to guns with fully concealed hammers. (I note that my humpback 38s DO have the second hammer block, even though their hammers are so shrouded I can't imagine what they could fall on that would put much pressure directly on the hammer.)