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Stories that are told by an "all seeing" narrator are told in the "third person."
Stories that are told by the main character, based on what s/he sees, are told in the "first person."
Suppose a story is told by a secondary character who is a friend of the main character. Examples are "The Great Gatsby," told by Nick Carraway, a friend of Jay Gatsby, or "My Friend Flicka," told by the owner of the horse. What is this persona/perspective called?
You're mixing up the terms.
There is the protagonist, and there is the narrator. Narration has perspective.
The narrator is the voice in which the book is told. If the story is told using "he/she/they" and not "I," it's third-person. This narrative voice (perspective) can see into everyone's thoughts (omniscient) or only one person's thoughts (limited).
If the narrator is using "I" and the story is only about what the "I" narrator sees, knows, and experiences, that's first-person. The story is told from one person's perspective.
The protagonist is the main character of the book. A book may have multiple protagonists (see A Song of Ice and Fire), primary and secondary protagonists (the Harry Potter series), or one protagonist.
The protagonist does not have to be the narrator. The narrator does not have to be the protagonist. You can have a first-person narrative, like The Great Gatsby or Song of Achilles, where the person who is telling the story isn't the most important person in the story. It's still a first-person narrative.
Typically, this is an Epistolary First Person (on wikipedia it's listed as Epistolary novel) if the narrator is presenting facts after they have happened in such a manner as to be read as a false document of events. The best known version of this is the character of Dr. Watson from the original Sherlock Holmes stories, who in the fictional universe, is the biographer of the fictional Holmes and the stories are his recollection of the case after the matter was solved. The general rule is that it must be presented as a primary source of events by a side character.
This is quite popular narrative voice in many classic horror and mystery types and can be found in Frankenstein, Dracula, and Dr. Jekyll and Mr. Hyde. It need not be an actual document, but the narrator must be telling to story to an audience after the fact (ala filing a police report or speaking to a news reporter. Frankenstein is an example of this type.). This is seen on visual medias such as the Merchant from Disney's Aladdin, possibley Cloppin from Disney's Hunchback of Notre Dame, and Future Ted from "How I Met Your Mother". The "Captain's Log" monologs from Star Trek may make the franchise lightly this as well.
In Gatsby's case, he is talking to a psychiatrist (I think, I've seen the movie more recently than I have read the book). I can't speak for your other novel.
it's called "as if told" first person.
