Meaning of 林 with 木 is exactly the same as Woods to Wood in English.
林 means woods.
林 is later extended to mean a large amount of similar things or people in a certain area, similar to woods formed with many trees.
Let us examine whether there is any difference in ancient times when 林 was created: (image get from http://www.vividict.com/)
|Learn one Chinese Character a day - 林|
Now let us enjoy a Chinese calligraphy with 林 inside: