How come that only revolver cylinders have thin walls? Why doesn’t the single shot pistols and derringers have thin walls?
Let's back up the bus for a moment. You have it backwards.
Revolver cylinders have relatively thin walls, much thinner than single shot pistols or derringers or rifles for that matter, because if the walls were a lot thicker the cylinder would have to be much larger in diameter. If the cylinder was a lot larger in diameter, the frame would have to be much bigger to house the cylinder. The gun would wind up being huge.
Now let's talk about the steel for a moment. It was not 'inferior', it was the best that was available at the time. Although craftsmen knew how to make steel for centuries, it was only made in small quantities and was very expensive. It was not until 1857 that the Bessemer process was developed that allowed steel to be produced in large quantities, inexpensively. You may not realize it but the frames and cylinders of many revolvers made during this period were made of iron, not steel. The same was true of many rifles too. And probably derringers and other firearms. In its most basic form steel is nothing but iron with a small percentage of carbon added. As time progressed, steel development progressed too, leading to stronger and stronger alloys. But for many years, iron, not steel was the metal used in firearm production. Colt's percussion revolvers had iron frames and cylinders, not steel. When the Colt Single Action Army revolver, chambered for 45 Colt, first appeared in 1873, the frame and cylinder were made of high grade iron, not steel. It was not until 1883 that Colt began using steel for the cylinder and frame of the SAA, even though this was 26 years after the Bessemer process made steel available at a reasonable cost.
The size and thickness of chamber walls in a revolver were adequate to contain the pressures generated by the cartridges fired in them. Period. There was no need to make them more massive, because the pressure generated by the Black Powder used in them was not as high as the pressure generated later by Smokeless powder.
Here is a photo you may find interesting. Left to right in the photo the cylinders are from a Pietta replica of the 1860 Army 44 caliber Colt Cap & Ball revolver, an antique Colt Richards Conversion revolver chambered for 44 Colt (yes 44 Colt, not 45 Colt), a 2nd Generation Colt Single Action Army revolver chambered for 45 Colt, a Ruger New Vaquero chambered for 45 Colt, and finally, a stainless 'original model' Vaquero chambered for 45 Colt. Chamber wall thicknesses at their thinnest point are Pietta 1860 - .050, Colt Richards Conversion - .037, 2nd Gen Colt - .042, New Vaquero - .045, and 'original model' Vaquero - .065.
Notice the center three revolvers have very similar wall thicknesses, .037, .042, and .045. I don't have the equipment to test it, but I will bet the Richards Conversion cylinder is made of iron, not steel. .037 between chambers was completely adequate to contain the pressure generated by the 44 Colt cartridge which contained about 27 grains of Black Powder.
The 45 Colt cartridge originally contained about 40 grains of Black Powder. Significantly more than the 44 Colt. Even so, the .042 thick chamber walls were strong enough to contain the pressure generated when the cartridge fired. It is interesting to note that Colt specifically did not factory warranty the SAA for the pressures generated by Smokeless powder until 1900. It was not until then that Colt felt the steel they were using at that time was sufficiently strong enough to contain the pressures generated by Smokeless powder. This SAA cylinder is made with modern high tensile strength steel, but the dimensions are pretty much the same as when this revolver first appeared in 1873. The Ruger New Vaquero cylinder is also made with modern high tensile strength steel. Both it and the SAA cylinder are plenty strong enough for modern 45 Colt ammunition that develops a maximum of 14,000 psi. Which brings us to the 'original model' Vaquero cylinder at the far right. You can see how much thicker it's chamber walls are than the New Vaquero. These revolvers were over built. They could take pressures far exceeding the 14,000 psi Max of standard 45 Colt ammunition. These revolvers could take the 'Ruger Only' loads specified in many reloading manuals.
Here is the rest of the story that has not been mentioned yet. The weakest part of most revolver cylinders is not the thin section between chambers. It is the thin section of steel between the bottom of the locking slots and a chamber below. Typically the metal is thinner here than anywhere else on the cylinder.
This is the burst cylinder from an antique Merwin Hulbert revolver. When the cylinder failed, the original point of failure was the locking slot. Once the failure began, the crack propagated along the thin section of metal between two adjacent chambers. Notice how the two adjacent chambers have begun to fold right where the locking slots are. A little bit more pressure and they would have let go too.
This photo shows how the top of the chamber separated from the rest of the cylinder. But the problem started at the location of the locking slot, not between chambers.
P.S. I just found the cylinder from one of my 1858 Remington Cap & Ball revolvers. Sorry, no photo, but the chamber walls are .042 thick at their narrowest point.