Trick question--you probably do both.
Personally, my ultimate audience usually falls into the "for others" category. But I do plenty of "for myself" writing along the way. For example, storyboarding. When I storyboard I just blurt out strings of punctuation-less, grammar-less word jumbles that make sense to me because they trigger memories of writing them.
For example, a snippet of a storyboard from a short piece I wrote a few years ago:
(Just reading that again is making me laugh.)@ drew k&k collaborate abt subjects note not much was exceptional about them except absent during lunch…k&k just making up doesn’t seem real when seven comes inseven informs them that she found location but not namesk&k make plans on when to talk to subs seven vetoes plans saying more time to scope out the situation and get into the groupK&k like okay more observing ......
But, see, I wrote it for myself, my eyes only. I had to transform it into something people would actually understand in order to make it acceptable in the "for others" category. It looked way different when I was done.
And that's okay! My point is, there are different stages. Writing is meant as a medium to convey an idea, a story, an emotion, whatever--and if you're just writing for, well, you, then there's no reason to use punctuation or capital letters.
Just thought I'd share that little revelation.