No: one could easily imagine a world where you remember all of the bad stuff, but are still incentivized to not write it down; an autobiography is an edited work of text, while autobiographical memory is a capability of a human.
You could remember bad stuff but you are not incentized to write it down.
Then how are they both different?
Won't there be a correlation?
Or am I missing something?
Bias on how you retell your own story is, as you say, a fairly obvious concern, so (for the purposes of this discussion) written autobiographies being biased is completely uninteresting.
Rather, it's the fact that your recollection of events biases towards the positive that's the novel, interesting information.