They mean the same but odsud can also mean away from here in:
Chci už být odsud. I want to be away from here.
There is also the bookish meaning of odtud as a cause as in English "From this follows that they had to..." "Odtud plyne, že museli..."
This is a small detail found in the dictionary, don't think too much about it. I am not even sure the difference is strict.