They seem to mean the exact same thing. Taken from the same dictionary:
–adverb Also, upwards
1.toward a higher place or position: The birds flew upward.
2.toward a higher or more distinguished condition, rank, level, etc.: His employer wishes to move him upward in the company.
3.to a greater degree;
The difference, is the usage of the words themselves in the different countries of GB and USA:
From the Chicago Manual of Style :
The preferred form is without the s in American English, with it in British English. The same is true for other directional words, such as upward, downward, forward, and backward, as well as afterward. The use of afterwards and backwards as adverbs is neither rare nor incorrect. But for consistency it is better to stay with the shorter forms.
So, it seems Americans prefer to use 'upward', while GB prefers using 'upwards'. This doesn't however, mean that everyone in USA uses 'upward', or everyone in Great Britain uses 'upwards'. It's a general reference.