I noticed that there seems to be a different connotation between these two words for ‘self’ and was wondering if anyone had more information about it.
自 looks like self-as-separate:
自営 as your own business (separate from the rest of the market);
自動 as automated (separate from other systems);
自由 as free (from other constraints)…
私 looks like self-as-private:
私見 your opinion that you may or may not share;
私用 something for your personal use;
私的 something proprietary or solely yours;
And then for extra fun, we have the triple hit of 私自身, picking up three separate connotations of ‘self’ and rolling them into something I’ve seen as ‘as for me…’ but it hits privacy, separateness, and then the body-as-self connotation of 身.
Maybe you are with 私自身. In that case 自身 is its own word acting as a suffix. And 私 is just a personal pronoun there. You can say ぼく自身 or あなた自身, or other versions as well.
Cool, I didn’t know you could use different pronouns with 自身. Thank you!
EDIT: If I’m right about 自 as a prefix, that would put 自身 into the first group. Which fits the duplication already present in it nicely. Maybe this pattern’s a real thing.