What is the difference in usage? What associations does the former word trigger that the latter does not (and vice versa)?
The NOAD reports that silviculture means the growing and cultivation of trees, while forestry means the science or practice of planting, managing, and caring for forests. If I say I am a silviculturist, I don't mean I plant forests.
The other grammatical difference between the words is that there are two derivates of silviculture (silvicultural, silviculturist), but there aren't derivates of forestry with similar meaning.
"Silviculture" to me, never having heard it before, just sounds like it's pretentious. Like a 'Garbage removal expert'.
I admit I'm outside my specialism, though, so there may be some distinction in the field. And I know people who are irritated by people calling themselves 'software engineers' when in reality they're just 'programmers' putting on airs...