The single action sear and the double action sear are 2 different things entirely. You can not compare the 2, as your post sounds. I have extensive S&W training and experience. You have some kind of "hick-up" going on with the lock work that I've not encountered in my 26yrs of working on S&Ws. The hammer would need a complete re-design to have 2 SA cocking notches. In DA mode, as the trigger is pulled, the hammer begins to travel. At a certain point, the hammer is "handed off" to the DA sear and the hammer continues to move back. With the continued pull of the trigger, the sear is released and the hammer falls. In SA mode, when the hammer is pulled back it should reach a point where the trigger has engaged the SA sear on the hammer. Notice as the hammer is pulled back, the trigger is moving, too. After the hammer is cocked with the trigger engaged in the SA sear, all that's required is to squeeze the trigger and the hammer should fall. There's a
'catch' in there somewhere that's acting as a 'sear'. No S&W I've ever worked on has 2 SA sears, but I don't see many "new ones", either. If I didn't have extensive training and experience, I wouldn't be removing a broken hammer stud in a "Smith 629, and installing a new one. Stud replacement is an 'advanced' job, usually sent back to the factory or sent to a gunsmith with advanced training in S&W Revolvers.