Like morte said, there is no answer because the question itself makes an incorrect assumption. Those all don’t have the same meaning.
Two important things to remember:
-
Just because an english dictionary or wk tells you a kanji means something, doesn’t necessarily mean it actually means that thing on its own.
-
When you get your meanings in a single english word, a lot of meaning and nuance can be lost.
I know you said you like etymology so I wish the answer had something more to do with that, but really it doesn’t. Not in these cases at least.
There has been some past discussion about the differences between 林 森 森林 specifically, and I’ll try to find that for you.
EDIT: Here you go. And in this thread I link to an even more in depth discussion