Your title seems different than everything you say in your post. So first, I’ll address your title:
If Wikilinks is turned off, and you make a link that exists OR make a new link that doesn’t exist, Obsidian will format a Markdown link to the title you typed.
If it isn’t behaving that way, you might have a plugin causing issues, and you should try it in the Sandbox vault to double-check.
Typing [[ is just a quick shortcut to form a link. The resulting link should respect the link format settings you chose.
You can also use the command “Add internal link”, and again, it will format the link as Wiki or Markdown depending on what you chose in your settings.
There is no distinction. You can use “Add internal links” or “[[” with either setting.
We have talked about this multiple times in the past. Most markdown links don’t work; a few do - #6 by rigmarole