In regards to writing, I personally don’t think I write in many places besides text messaging and papers for classes, however the place I often write in would be my notes app on my phone. The writings I have within my notes I want to be kept private which either means it’s just for me to read or have a few select people read. The reason I want them to be kept private is because of the fact, they’re either ways of venting my frustrations about something, a message I want to send to someone that I want to review/revise, or they could be ideas for stories I want to write about later down the line. If my notes were to be moved from a private to a public location, then people would be able see how I feel about the problems I face in day to day life, my ideas for stories I want to write and the very vulnerable messages I send to my friends and family.
Now with text messages, I assume them to be private because it’s a conversation about a variety of things with that one person I’m talking to and depending on the person, with the subjects of those messages being very sensitive. However, if I were to be more honest about my assumption on the privacy of my text messages, I feel like they could either be public or private. I’m saying this because I understand how easy it is to screenshot or share messages whether they could be funny, serious, etc. since I do it myself from time to time. If we go with my original assumption that my text messages are private, the implications of them becoming public could result in many conversations possibly hurting/offending other people’s feelings, or even possibly the opposite since people could find out how I feel about them but didn’t know because I may have never expressed those feelings before.
One more location I often write would have to be twitter. With twitter, I assume my posts would be private, in regards to not having any family members seeing them since none of my relatives have a twitter account. (At least not that I know of.) I would consider my posts to be private since I could post very odd or strange tweets/videos that I know my family members wouldn’t understand since we most likely don’t share the same sense of humor. Now if my tweets were to become public, I’d probably get really funny or strange looks from my family since these videos wouldn’t make sense to them.
I completely forgot that text messages are a form of public and private writing as well. I agree with your assumption that your assumed “private” texts could become public when people screenshot and share it with others.