It's been a long time coming, but as promised, here's a mini lesson on the difference between subjective and omniscient narration!
I first wanted to address this because I keep seeing people call any subjective narration "first-person" narration. In case you missed it, I covered the definitions of first-person and third-person narration in another mini lesson. The bit to remember for today is that "first-person" simply means the use of first-person pronouns: I, we, us, etc.
Subjective narration is when a story is told through the lens of one character's experience at a time. There can be multiple narrators or just one, but each perspective is limited to what the narrating character sees, hears, feels, knows, etc. In fact, another term for subjective narration is limited narration. It places the reader into the body & mind of the narrator, so we experience the story unfolding along with them. This is the more common type of narration seen in fiction nowadays.
Omniscient narration, on the other hand, is when the story is told by an all-knowing narrator. This narrator can dip into different characters' minds and also share with the reader things the characters may not know at all. Everything we may need to know about the world, the characters, and the plot, this narrator knows. While less common nowadays, it is no less powerful a choice, and both types of narration have their strengths.
Both types of narration can be either first- or third-person. However, it's extremely rare to have a truly omniscient first-person narrator. Such narrators often turn out to be unreliable, meaning the reader can't necessarily trust what they're saying and may need to draw separate conclusions about conversations and events. An unreliable narrator might simply misconstrue events and other characters' words and actions, or they may intentionally conceal information from the reader, misrepresent events, and even lie outright. They may also be suffering from mental conditions which affect their perception of events. But an unreliable narrator may still present themselves as an omniscient (or even objective) one.
One last thing to note is that narrative tense—whether the story is told in the past, present, or even (and extremely rarely) future—is independent from whether the narration is in first- or third-person and whether it's subjective or omniscient. So there are many combinations with which you can experiment in your writing!