They're both correct. The first one treats "update" as a noun, emphasizing the final product. The second one uses a verbal noun (the gerund "updating") to emphasize the process itself.

Thanks for the update/ Thank you for the update.

I would say either Thanks for the update. or Thanks for updating me. I think "updating" needs an object, but I don't know how to prove this other than what sounds right (to me).

They are both correct but I'm guessing you need the first one to thank someone for the update of in another way, for giving you the latest news