While they are similar skills, they don't always go along together. One of the goals of the scriptwriting craft is to learn to do both.
These strengths (or weaknesses) are always more apparent when studying someone else's dialogue than when evaluating your own. At least it is for me. And it's most noticeable when learning a part.
Memorization of a part takes a very concentrated effort and an intimate, possibly word-by-word study effort. While scriptwriters don't always create speeches one word at a time, very often, the actors playing those roles learn the scripts that way. And in so doing, often discover meanings in the speeches that may not have been intended.
When I have acted in my own scripts, I find this out first hand. And while I can usually learn most parts quickly, I am generally slower when working on my own scripts. I think that's because I'm doing the double duty of learning the role, and also keeping my scriptwriting cap on and evaluating the script at the same time, trying to determine if I've written it the best way.
I generally liken learning roles to learning songs. Each speech can have a beginning, middle, and end. There are techniques to remembering lists of items, or listening for cues from another actor's previous speech.
Whatever the approach, though, knowing what actors go through to learn a role is a key element in scriptwriting, in keeping in mind the challenges of learning scripts, and in learning what makes one script more actor-friendly than another.