A cat’s tail is all three of the above. It is made up of bone, muscle, blood vessels and nerves just like the other parts of a domestic cat’s body. It is no more or less sensitive than the other main areas of the cat’s body in my view. But clearly it should not be grabbed and pulled. It should be respected like the rest of a cat’s body.
The cat’s spinal column is made up of vertebrae which lead into the tail and each vertebra of the supple tail articulates (is able to move in relation to the adjacent vertebra). A domestic cat has 19-23 vertebrae. This represents about 10% of the total number of bones in a cat’s body.
The spinal cord is protected by the vertebrae of the spine, which passes from the head down the spinal column and into the tail. The spinal cord and peripheral nervous system contain billions of cells called neurons which connect to each other to form neurological circuits. They carry signals back and forth from the brain to the extremities including the tail.
The tail muscles are called sacrocaudals and intertransversarials. They raise, lower and curl the tail. When you see a domestic cat wag their tail because of indecision all the elements, which I have referred to, are functioning.
Blood is carried into the tail within an artery which is muscular and elastic and returns from the tail in a vein. The amount of blood that the tail receives is controlled by nerves and hormones which cause arterioles to dilate in response to local activity and which dramatically increases the blood supply to that region.
In general terms the sequence is as follows. The cat’s brain is indecisive about whether to attack a prey animal or hold back. The mind is in balance. Subconsciously, the cat believes that they are physically trying to balance on an object. The brain sends a signal down the spine to the central nerve running down the middle of the tail. This signal is transmitted to peripheral nerves in the tail connected to the tail’s muscles. These nerves stimulate the muscles to contract and expand which wags the tail. The tail is able to move like this because the vertebrae can be articulated, one in relation to the other, as mentioned. The blood flow is increased to supply oxygen and nutrients to the muscles.
And if a person abuses a cat and pulls their tail, the peripheral nerves of the tail send a message to the central nerve and then down the spinal column to the cat’s brain to signal pain. The purpose of signalling pain is to tell the cat that the tail might be injured and to take steps to prevent further injury. In order to protect the tail, the cat will try and escape from the situation which is potentially causing the damage. This is the person who is abusing the cat. The cat will turn and swipe at the person and try and release themselves from the person’s grip.
Postscript: the cat’s muscles mostly consist of fast-twitch fatiguing cells. It is these muscle cells which give the domestic cat speed of movement. The muscles of their limbs contract very rapidly.
Postscript 2: people ask whether the cat’s tail is a limb. I would say that it is not a limb because it doesn’t act like a normal limb. These are the four legs of a cat. The cat’s paws attached to limbs can grab and hold objects. Tails cannot do this. However, when a domestic cat loses their forelegs or has malfunctioning forelegs, they may use their tail far more in order to stabilise themselves when, for example, standing up. At this stage their tail is starting to enter the definition of a limb.