Chickens may run around after their head is cut off if the head is severed near the base of the skull leaving the brain stem intact and missing the jugular vein. This usually only lasts for a few minutes, however there is the case of Miracle Mike that survived for 18 months after his head was cut off. Do turkeys also exhibit this same behavior and if not, what makes this possible in a chicken but not a turkey?
The brain does not control all bodily movements. Some movements are to a great extent controlled by neural networks in the spinal cord. The spine contains a network which is pre-programmed to control the muscles in frequently-used movements such as running or swimming in chickens. This is why a chicken can run away after you chop its head off. Likewise, turtles swim using their a spinal neural network. As long as a signal is received somewhere in this network, the network will activate the swimming movements. Such a system is coined an ‘attractor network’ (source: Science Nordic). A similar system has been shown to occur in a sea slug. I couldn't find similar information in the turkey though. Happy Thanksgiving :)
Note that walking and running in higher animals (mammals) is controlled by the motor cortex higher up in the brain, involving a more complex system including the pyramidal system. Reflexes, however are controlled by quick, short spinal relay circuits in higher animals as well.