I am writing a first-person story, and I am having trouble showing the difference between narration and the thoughts of the character. To expand on this: I mean to separate the thought of the character in the moment. Not at the time the narrator is talking.
So, between what my high school creative writing teacher told me was the norm, and what I've been doing personally, I recommend using normal text for narration, and italics for thoughts.
In a story I'm writing, I have the main character is retelling the story and someone is writing it down. (And since most stories are written in past tense, this should apply for your format). Most of the text is narration from this "future" perspective, and is formatted as normal text, but in some cases the character/me (the author), also shares their thoughts, from that exact time, and I signify that with italics.
Paragraph from said story.
Then the door started to slowly open. Holy crap! I thought, This is crazy! Where the hell did the door come from? Of course the door could have just been my imagination. In that other world, I had always been having weird dreams, and strange imaginings of magic and of another world. It reminded me of the doorway to Narnia, or was that a wardrobe? I can’t remember anymore. But then I remembered, Narnia, is just a story, fake, not real.
You don't necessarily need to distinguish the two. If you write, for example,
Dan stared out of the window of the classroom. A green park spread outside. Tulips and Hyacinths were in full bloom. Inside, the teacher droned on about something.
You are both narrating the setting (classroom, spring), and showing the character's boredom and desire to be outside.
I'm not entirely sure what you mean, but I'll interpret it as distinguishing between thoughts of the first-person narrator as character when the story happened, and the thoughts of the narrator when narrating it.
This concept in my opinion only makes sense if the the narrator tells the story in the past tense, as telling in the present tense implies that the events of the story are happening right as they are told, and therefore the thoughts during narration are the thoughts during the events of the story.
For first-person past tense, it is easy to make the distinction, by using the appropriate tense: Thoughts the character had back then are past thoughts, and therefore are told in past tense. Thoughts the narrator has during narration are present thoughts, and therefore are told in present tense.
The door opened, and a man came in. I thought it was Tom.
Here the character, when seeing the door open, was of the opinion that the man entering the room was Tom (and the formulation suggests that it turned out not to be Tom).
The door opened, and a man came in. I think it was Tom.
Here the narrator thinks the person who came in back then was Tom, but is not sure. There's no indication that at the time the story happened, the identity of the person entering was unclear; it's the narrator's memory that's failing.