Some movement is simply a response to a stimulus. If you touch a snail, it will draw up into its shell but humans are not simply machines of stimulus and action; almost all the voluntary movement we perform is goal-directed, meaning it has a purpose that is determined by the person moving. Say for example, you are removing your thanksgiving turkey from the oven and you scald your arm because the lid tips open.
Absolutely true - motivation is really key in thorough TBI recovery. It can be a ton of hard work, so finding the resources to keep up the necessary hard work is paramount. And not only in the initial stages, but later on, when you're "supposed to be better"... but things aren't going quite as well as you'd like/hope/wish.