Colt since 1905 and S&W since 1945 actually have TWO internal, automatic safety systems.
First is the Rebounding hammer.
Pull the trigger on an pre-Mark III Colt revolver or a S&W and release the trigger slowly.
As the trigger is released you'll see the hammer forced backward or "rebounded".
The hammer is pushed backward away from the cartridge and then locked there so it can't move forward again until the trigger is released and pulled again.
Since there was a chance that if the hammer was struck hard enough the rebound feature could break or be forced, both Colt in 1905 and S&W in 1945 added a Hammer block safety.
This is a steel "L" shaped lever in front of the hammer.
When the trigger is pulled, the safety lever is pulled downward, and allows the hammer to move forward to fire the cartridge.
When the trigger is released, the level is pushed back upward in front of the hammer to block it from moving forward again.
Unless the trigger is held back the lever moves upward again, so even if the rebound feature is damaged, the hammer is blocked from moving forward.
The more modern revolver safety system was invented around the turn of the last century by Iver Johnson, and updated and refined by Colt in 1969.
This is the transfer bar safety-ignition system.
The system as refined by Colt was so good every double action revolver invented since uses a near copy of it.
This system works only in a revolver with a firing pin mounted inside the frame, not on the hammer.
In this system the hammer is machined so that it CANNOT actually contact the firing pin. In it's forward at rest position the hammer is resting on the revolvers frame, and has a hole in the hammer face or a projection on the hammer that totally prevents it from touching the firing pin.
The safety-ignition system is a flat lever-like plate that's attached to the trigger.
When the trigger is pulled the plate rises UPWARD in front of the hammer.
When the hammer falls it strikes the flat plate which in turn strikes, or transfers, the force to the firing pin to fire the cartridge.
If the trigger is released, the transfer bar is snatched downward from in front of the hammer and the hammer can only strike the frame not the firing pin.
Since this system is both an automatic safety and the ignition system, these are much simpler, stronger designs that are much easier and faster to build.
Both the older rebound and safety lever design and the modern transfer bar systems are as safe as it's possible to make a machine, therefore both are perfectly safe to carry with all chambers loaded, since the only way to get the gun to fire is to deliberately pull the trigger.