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I'm not a musician, and I know basically nothing about music, and music theory and what-not. (I basically just know a few common terms, and how to play chords)

In most songs with two or more people singing, (Duets specifically) the singers almost always sing in harmony, but not the same notes. What term is used to describe this? I want to be able to learn how to do it, but I don't know the specific term to do more research on it.

The term "harmony" itself is what you are looking for.
Being able to sing in harmony (2 or more different voices) with someone however doesn't require any more skills or theory than singing alone or in unison (same notes, only one voice) because everyone learns "his notes" as he would do singing alone. The only thing I could think of is having a good ear, maybe good relative pitch, but that is required for soloists singers too.

The hard part is composing or improvising the harmony and that requires a lot of different music theory skills, not only the harmony part. If this is what you are looking for, I would suggest to start with generic music theory or if you are really serious about it, take piano lessons.

Singing together but different notes is singing in harmony. Singing the same notes would be singing in unison.

From a strictly music theory point of view, one might call it counterpoint. The original Latin phrase "punctus contra punctum" (note against note) denotes just that. The term indicates two or more voices, each having their own independent melody (the horizontal aspect in written music), resulting in a harmony (the vertical aspect).

It is called polyphonic singing aka overtone chanting, harmonic singing, or throat singing. Bjork does some (but NOT all) of her singing in a polyphonic manner.

Also refer to Wikipedia documentation as follows:

Overtone singing – also known as overtone chanting, harmonic singing, or throat singing – is a type of singing in which the singer manipulates the resonances (or formants) created as air travels from the lungs, past the vocal folds, and out of the lips to produce a melody.

The harmonics (fundamental and overtones) of a sound wave made by the human voice can be selectively amplified by changing the shape of the resonant cavities of the mouth, larynx, and pharynx.[1] This resonant tuning allows singers to create apparently more than one pitch at the same time (the fundamental and a selected overtone), while actually generating only a single fundamental frequency with their vocal folds.

 Each note is like a rainbow of sound. When you shoot a light beam through a prism, you get a rainbow. You think of a rainbow of sounds when you sing one note. If you can use your throat as a prism, you can expose the rainbow – through positioning the throat in a certain physical way, which will reveal the harmonic series note by note.[2]

https://en.wikipedia.org/wiki/Overtone_singing#Mongolia_and_Buryatia