jmc

Grouping the corresponding terms in $A-B,$ we can write $$A-B=\left(\lceil {\log }_{2}2\rceil -\lfloor {\log }_{2}2\rfloor \right)+\left(\lceil {\log }_{2}3\rceil -\lfloor {\log }_{2}3\rfloor \right)+\cdots +\left(\lceil {\log }_{2}1000\rceil -\lfloor {\log }_{2}1000\rfloor \right).$$For a real number $x,$ we have $\lceil x\rceil -\lfloor x\rfloor =1$ if $x$ is not an integer, and $\lceil x\rceil -\lfloor x\rfloor =0$ otherwise. Therefore, $A-B$ is simply equal to the number of non-integer values in the list ${\log }_{2}2,{\log }_{2}3,\dots ,{\log }_{2}1000.$

The only integer values in the list are ${\log }_{2}2=1,$ ${\log }_{2}4=2,$ and so on, up to ${\log }_{2}512=9.$ Since there are $999$ numbers in the list and $9$ of them are integers, the number of non-integers is $999-9=\boxed{990}.$