How is the alpha carbon defined in alkyl halides?
The &#x3b1; carbon is the one directly attached to the functional group. There is no contradiction to your book’s claim that the &#x3b1; carbon of 2-bromobutane is the one directly bound to bromine.

This is due to the different definitions of functional groups and what they include. The keto functional group is defined as $\ce{-C(=O)-{}}$, i.e. it includes the carbon atom doubly bonded to oxygen. Halogen functional groups, for example the bromo functional group are defined as only the heteroatom, so in this case $\ce{-Br}$. Note that because the carbon is not included in the definition of this functional group, it is instead the &#x3b1; carbon.

This means that reducing the ester functionality of a &#x3b2;-halo ester will result in a &#x3b3;-halo alcohol even though no group migrated.