The apparently contradiction really isn't one because the tables are going in different orders.

For example, the first table goes "mir, dir, ihm, ihr, ihm" for "ich, du, er, sie, es".

In contrast, the second table goes "mir, dir, ihm, ihm, ihr" for "ich, du, er, es, sie".

The only difference is that the second table, for no apparent reason, chose to write "er, es, sie" instead of the typical order of "er, sie, es." That's all.