If a game is designed in such a way as to have the player take control of a main character, and experience the 'game world' through that character, where is the distinction between self-inserting and not self-inserting?
I think the difference is that a self-insert is literally meant to be you, and the latter is just your avatar.
In choice-heavy games like
Fallout: New Vegas and
Undertale, your first run or so might have you self insert as the protagonist, and choose as you would in that situation. However, your next runs become more and more about seeking each bit of content available. Maybe this run I'll see what the Legion is about, or maybe I'll spare all the monsters this time. The protagonist stops representing you and becomes more of an avatar for experiencing the game's content.
For 'self-insert' games (which I can only really find examples of here), the choices you can make are less radical. No matter the choices, the protagonist can still somewhat represent you. You usually can't go on mass-muder rampages or join terrorist organizations, because that's what an avatar seeking to experience everything would want to do, so the game doesn't let you.
Of course, I am a little biased about this so maybe I am wrong.