The transposition theorem says that if we take a filter diagram and reverse all the elements - swapping the order of execution for every element, and reversing the direction of all the flow arrows - then the result is the same:
For this reason, direct form 1 is often called transposed direct form 2.
Don't ask me why these terms seem to be as confusing as they possibly could be - I didn't make them up. I imagine mathematicians sit around at coffee break and come up with new ways to spread despondency amongst us lesser mortals. Here are the two main sources of confusion: