They are really very similar and I would have to think of specific examples to see if there are subtle differences in usage.
It sounds more natural to say "the table is made of wood". But if the table had woods of different origins, you would say "the table is made from various woods".
There is an advert in the UK for a soft drink which is described as being "made in Scotland - from girders". Obviously you don't drink girders so a process is implied.
So you could explain the difference between the examples here as follows: if an object is made of just one material, then it is "made of". If an object is made using a more complex process, perhaps involving several materials, then it is "made from." I am happy that my examples show correct usage but my conclusion is speculative, so please beware!