Edgar Allen Poe's "The Purloined Letter" uses a first person narrator who, by definition, participates in the story and only knows his own motives, thoughts, perceptions, feelings, and emotions:
At Paris, just after dark one gusty evening in the autumn of 18--, I was enjoying the twofold luxury of meditation and a meerschaum, ...
Herman Mellville's short story "Bartleby the Scrivener: A Tale of Wall Street" also uses a first person narrator who is, also by definition, a participant in the story and only knowledgeable about his own thoughts, motives, feelings, perceptions, and emotions:
I AM a rather elderly man. The nature of my avocations for the last thirty years has brought me into more than ordinary contact with . . . the law-copyists . . .
In first person narration, the narrator refers to her-/-imself as "I," and the narrator only knows about the inner world of other characters if they tell her/him, if s/he infers or deduces or guesses at it, or if they read a letter or a diary entry or explanatory article etc, or if some other character tells them something about it.
Third person omniscient narration differs greatly from first person because the narrative is told by someone who is not a participant in the story and has the ability to know the inner world of any character, thus can tell the thoughts, feelings, perceptions, motives, emotions of any character, and can tell the story through the experience of any character at any moment in the narrative (change the point of view at any time). As can be seen, by this definition neither Poe's story nor Melville's story has a third person omniscient narrator.