Thanks for writing back, Porpoise.
In my conscious state, it appears to me that my mind, which performs thinking and recognizes that it is thinking, and is a real subject.
If my brain dies, I still have my physical brain, but I don't have a working mind anymore and am not thinking, and so the remaining physical brain and the mind and its processes are distinguishable. Like you said, if my legs become paralyzed (eg. a parapalegic), I still have the physical legs, but I don't have the walking.
The difference in the two situations is that I sense that I have a physical brain and a mind that both work together to process thinking and are distinguished by the process of death, whereas I sense only my legs when it comes to walking.
Unlike the processes of walking and thinking, I sense that my mind is the subject that performs the actions with the help of the brain. Thus the physical subject brain, the subject mind, and their tasks of thinking are each distinguishable from each other.