could be anything.... most engineers use generic terms like this once they define it earlier in a report so they don't have to repeat themselves.
off the top of my head .... soil stabilization could be chemical, subgrade strength, or deal with slope failure.
soil modifying could be just about anything.... adding/drying moisture, compacting/tilling, mixing in aggregate or lime.....
For calcium based stabilization (cement, lime, lime kiln dust), modification generally means adding a little chemical to help dry out the soil and allow it to be compacted. Stabilization requires more chemical so that you get some bonding of the soil and gain strength that way. For cement, you are generally using 1-2% (by weight) for modification and 3-5% for stabilization.
You can modify soil without stabilizing it; however, you cannot generally stabilize soil without modifying it. Modifying soil is changing it in some manner. Stabilizing soil results in a greater resistance to load deformation.
For pavement subgrades, we typically referenced stabilization when using lime and modification when using cement to improve the subgrade. But this is pretty much a firm preference, not even regional, necessarily. I agree with others that the correct answer is "it depends...".
'Improve' is another word that can be interchangeable with modify and stabilize in most cases.