What is the difference between a Whakatauki and Whakatauaki?

You are very close! "Whakatauki" and "Whakatauaki" are actually the same word. It's just a matter of spelling!

Whakatauki is the correct spelling of the Māori word for proverb or saying. It can also be spelled Whakatauaki, but the former is more commonly used.

So, there is no difference between the two. They are both used to refer to Māori proverbs and sayings.