Actually, I didn't know the difference between them because I didn't have this quiestion. I was looking for the explication on internet and there are various opinions. The one I agree with the most is the opinion based on thier pronunciation. According to the opinion, the place the trees grow is called 林 and the swelled land with trees is called 森. According to other opinion, the place with tree cared by humanbeing, for example, plant or cut the tree, is 林 and the one is wild trees, completely narural is called 森, however, there are words 原生林 or something that means "wild / without being cared by human being". After all, I didn't find any specific difference. I hope this was helpful a bit and other people answer to you.

森 has many trees more than 林. You can imagine that from its Kange. In addition, 森 is kind of complete natural, on the other hand, 林 has been taken care by human. Anyway, they are similar.

Ooops. I made a typing error, sorry. × Kange →　○ Kanji

林 is wood and 森 means forest.

:cough: Wild guess: 'mori' is a bigger forest than 'hayashi'? My kanji dictionary even gives them together as 'shinrin', with the same meaning, forest, wood...