Not only does grading involve "moving dirt"
but it usually involves either import or export
to a certified dumpsite.  The most popular
local site is Camp Pendleton.  Depending on
local needs at the time of export, a closer site
with lower fees may be possible.  
straddles an area of "cut" and an area of "fill".
The concern is potential uneven settling.   As
a result, the entire site is "over-excavated" to
a depth specified by the soils engineers
(typically 5 feet) and re-compacted.  Any
subsequent footings (or slab) will then be
entirely in fill and if there is any settling, it can
be expected to be uniform, minimizing any
chance of future cracking.