There's a lot of confusion over the issue of shutter tape. I hope the following will answer all of your questions. If not, please let me know so this section can be improved.
In the pre-war Contaflex TLR and early Contax I cameras Zeiss initially used a shutter tape made of cotton. This tape failed quickly and was replaced with a silk tape which was also used in the later Contaflex TLR, Contax I models and the II and III camera models. This silk tape did not change in any way while these cameras were being made.
In the pre-war Contax TLR, II and III cameras the shutter tape is a directly participating shutter component that actively participates in the process of shutter speed. This process involves friction and this is why the original cotton tape did not last long in service. In designing the silk tape Zeiss specified a particular silk fiber (one of a possible 1500 types), a particular weave, and specific dimensions. All of these were maintained within very tight manufacturing tolerances.
In the post-war Contax IIa and IIIa cameras Zeiss designed a totally different shutter within which the shutter tape does not participate directly in shutter speed. In the initial Contax IIa models the tape was made of cotton dyed black and then later the material was switched to nylon fiber. The cotton tape tended to stiffen with age due to the chemical effects of the dye used to color it black. While the tape does not directly participate in shutter speed, it can effect shutter speed accuracy if something is wrong with it, and the stiffness of the aged cotton tape caused problems with the higher speeds.
In both the pre and post war cameras the shutter tape connects to the right and left sides of the upper shutter curtain to connect the curtain to its springs that pull it down when the shutter is released. The tape in the pre war cameras tends to fail by sudden breakage and the tape in the post war cameras fails due to fraying.
The breakage of the pre war tape is caused by the damage done by the friction necessary for the tape to participate in the shutter speed process. The fraying of the post war nylon tape is caused by the lower curtain sliding down on the top side of the tape when the shutter is released. The fraying interferes with the lower shutter curtain when it descends and can cause problems with the faster shutter speeds. It can also cause problems with the curtains not lining up precisely when the shutter closes.
A pre-war camera in original condition with bad tapes is very common. About 10% of the post war cameras have nylon tapes that are excessively frayed.
When the Russians seized the Contax II and III camera design at the end of World War II they produced a small number of cameras using German parts seized from the Jena works. But the original silk tape ran out and it had been made for Zeiss in Japan and the manufacturer had been destroyed. The Russians changed the tape to be made of nylon. But this tape is much thicker than the original silk tape and so the design of the Kiev shutter was changed to accommodate this tape. The shutter springs were made of thicker diameter wire and are stronger. The parts of the shutter through which the tape passes have been made larger. The Russian tape will not work and may cause irreparable damage if it is used in a Contax camera. The Contaflex TLR and the Contax 1 cameras are particularly liable to irrepairable damage if the wrong tape is used in them.
The reason the Contaflex TLR and the Contax 1 are very sensitive to the tape used in them is due to the fragility of the shutter curtain latching mechanism used only in these two models. These two cameras use thin steel friction pincers located in the upper lip of the bottom curtain. If the shutter springs are overly tightened the upper curtain lip can hit these grippers on their edge and bend them. The grippers are riveted permanently to the edge of the curtain so repairs are always risky and difficult. If thick Russian tape is put into a Contaflex TLR or Contax I the shutter will have so much extra friction due to the excessive thickness of the tape that the springs will have to be tightened to the point where latching pincer damage is a sure thing.
I spent three years and $5,000.00 to obtain a supply of silk tape made out of the same exact single fiber Zeiss used and to have it woven by the same weave and to the exact same dimensions. This would not have been done if extensive testing had not demonstrated conclusively that there was no other way to get a Contax to act like a Contax when its overhauled. Don't let anyone fool you. Just anything will not do, and it can do a lot of damage. Zeiss took great care to ensure the uniformity of the silk tape they used over the years they used it and they would not have done this if it wasn't fundamentally important and absolutely necessary.
These days a many workers are taking a short and very dishonest route to getting a prewar Contax II or III into "working" condition. This is to just take out the original Germany made Contax shutter and substitute it with a russian made Kiev camera shutter. There is a false folklore circulating among some people to the effect that the Kiev shutter and the Contax shutter are the same but nothing could be further from the truth. Kiev incorporated a flash synchronization electrical contact board inside their shutters. To accomodate this board the shutter frame was made slightly wider than the Contax shutter. This extra width causes a constriction when a Kiev shutter frame is forced into the smaller space of the Contax body and as a consequence of this the shutter springs must be greatly overtightened to get the shutter to work and it is not accurate, reliable or long lived. Then there is the problem of workmanship. The russians were apparently incapable of making shutter parts or a shutter whose quality even begins to approch that of the original Contax German machine. Put them side by side and you will quickly see the Kiev shutter is a real piece of junk.