Until very recently I'd though a chord was any group of notes played together.
However, I just heard a chord defined as "three or more notes played together."
If this is the case, what should I call just two notes played together?
From my experience, there is no one 'best' term for two notes played together that is universally (or near-universally) agreed-on.
dyad is the most specific term for a pair of pitches sounding together, but it's not commonly-used.
interval works for many, but others will say that is a term for the distance between the notes, rather than something that refers to the act of playing them together.
some will say that chord is fine for two notes, and that seems to be the case for specific usages like the term 'power chord'.
on stringed instruments one may talk about playing a double-stop, although that's a reference to the playing technique rather than the pure concept.
So basically, whatever term someone uses, you have license to be a bore and tell them they're wrong.
A Chord is what happens when you play or sing more than one note at a time. 2 note chords are called partial chords. 3 note chords spaced by thirds and fifths are called Triads. Triads are not ambiguous. e.g. CEG is an unambigous C Major triad. The idea behid so called partial chords is that thay are ambiguous. For example C and E are notes in both the C Major (CEG) and A Minor (ACE) triads. CE is a partial chord with no name.
A special case of this is so called '5' chords which do have a name. G5, for example is comp\osed of the notes G and D. It's called G5 because it contains the root G and its perfect fifth D. Since it has no third to tell whether it's Major or Minor it's still ambiguous. Rock Guitarist like these chords.
Just to be super clear: partial chords are bits of triads (usually), and Triads form the "cores" of larger chords (like Am7).
Ultimately there is no unanimous definitions for these words, so it's useful to know how they can be used.
One definition has a chord being three or more notes. This means that having only two notes wouldn't be a chord but would be an interval.
As someone else pointed out, power chords are a thing and consist of only two pitches (though they may run through several octaves). It seems entirely reasonable to call such an interval a chord since it is functioning as one. Which leads us to a definition based on function.
If your note aggregate under question functions as a chord in terms of voice leading and harmony then it would be a chord and an interval could then also be a chord. But, just having three notes sounding at the same time would not necessarily be a chord if they are not functioning as a chord re voice leading and harmony. Such a collection would just be a note aggregate or potentially a cluster.
In summary, you can define chords in terms of numbers or function. An interval is always two pitches (though they can be the same exact pitch!) and can be considered a chord in certain circumstances/definitions. Under other circumstances having three or more notes might not be considered a chord but an aggregate or cluster (or even more confusingly a cluster chord!)
You'll hear and witness any and all of these usages so it's good to be aware of the many different ways these terms are used.
Melodic and Harmonic intervals:
“Melodic” means played one note at a time, either ascending or descending in pitch. “Harmonic” means both notes are played together.
In addition to @topomorto's answer you could also use "implied harmony." For example, G over B moving to E over C (all naturals) implies a G major chord going to C major even though the fifths of the chord are missing from the implied triads.
I prefer this definition which simply defines chord as a harmonic entity of multiple pitches (indefinite quantity.)
If you want to refer to one of those chords as triad etc...
The actual answer is "An Interval." Of course, that isn't a complete explanation. An interval may appear on its own or as a representative of a chord. For example the interval C-E by itself is just a major third. In a piece of music it could stand for a C major chord, and A minor chord, depending on the voice leading. It could just be an incomplete chord. A fifth C-G can, with enough distortion be a Power Chord representing C major (or minor).
Yes, the nomenclature is not perfectly agreed upon. But we simply have to deal with that. How about simply stipulating what the tones are, and not agonizing over whether it's an "interval" or a "chord". The definitions are not going to help tell you what it "is".
Harmonic interval = two notes played simultaneously.
Chord = three or more notes played simultaneously.
These definitions are universally accepted. It's physics, much like GPS triangulation; it is not possible to determine the root let alone the type of chord unless you have at least three notes.
When teaching young students, just call them all chords and explain that two note chords have lots of different names. Then get on with it.