What is the difference between the two?
Duality Principle states that any theorem in switching algebra remains true if 0 and 1 are swapped and + and . are swapped throughout.
DeMorgan's Law says that any theorem remains true if the variables are complemented and + and . are swapped as well.
I don't see a difference really, could anyone enlighten me?
In your formulation, the two items indeed seem to say the same with very minor changes in wording.
However, you're quoting De Morgan's laws wrong. What they are usually taken to say is that $$ \neg(A \land B) = \neg A \lor \neg B \\ \neg(A \lor B) = \neg A \land \neg B $$ (or something very similar to that) are identities.
These laws imply the duality principle that you're speaking about, but the duality principle itself will not help you conclude from whole cloth that $\neg(A\land B)$ always has the same truth value as $\neg A\lor \neg B$ -- because which already known identity would you apply it to from the beginning?