A while ago I happened to see a very silly comedy show (お笑い番組) on Japanese TV, where - among many useless jokes, fake laughs and endless commercials - this question came up and got an excellent explanation, which saved the whole thing from being a total waste of time.
Apparently it's not just a question of size. According to the guy who talked about this on the show, the difference is that 林 is used for an area covered by many trees belonging to a single type, whereas 森 is a real forest with all kinds of trees growing together. So if you see a large expanse of land covered exclusively with 杉 trees, it's a 林. Of course there can be the odd "outsider tree" in the middle of this, but that's the principle.
Based on my own knowledge too, this seems like a plausible explanation.
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