All the notes of a piano can fold down into one set of twelve notes, beginning at C and ending at B - or beginning anywhere else if you really prefer. There are several C notes, each of which is precisely a 2:1 ratio (an octave) of another C note, and for that reason the body treats them quite identically. We'll just fold them down together, and get:
{c C d D e f F g G a A b} (where lowercase is natural and uppercase is flat)
Now, what makes a chord? A chord is any three or more of these notes played at once - with the exception of {c g} and its transpositions - which have only two. This chord describes an interval of a perfect fifth, which is a "fifth" because {c d e f g} is five scale degrees. A perfect fifth describes a 3:2 ratio damn near exactly. The other intervals, the seconds, thirds, fourths, are not so nice sounding at all, so we do not ascribe to them special statuses, they are only "intervals", not "chords" - but {c g} is a chord.
If we define a chord this way, then every chord you will find in music can be described as featuring a perfect fifth somewhere - or else, a diminished fifth (as {C g}) or an augmented fifth (as {c G}). The chords without any fifths whatsoever, such as {c C d D}, are simply disgusting and have no place in even the edgiest music. You won't find them anywhere.
This fifth that one finds in a chord will have a root, as {c}, and a "dominant" above it, as {g}. They sound the same. One could mistake the one for the other. But they don't sound the same the way a C note and the next C note above it will sound the same, no, not at all. The {g} feels to be above the {c}. Try it on HTML Piano if you have no instrument. Play a C and a G.
The interval between {c} and {f} (or between {g} and the {c} above it) is a perfect fourth, damn near identical to a 4:3 ratio. They sound the same. But they don't sound the same the way an octave or a perfect fifth sound the same. The {f} feels to be above the {c}, but lazily so, not as much above as the fifth was.
The interval between {c} and {e} is a major third. It does NOT sound the same. Not at all! For NOT sounding the same, we do not permit a major third alone to call itself a "chord". But it is useful inside of a chord - so though we feel free to call our perfect fifth a chord - traditionally a "power chord" or as I would call it, an empty chord, we can fill that empty chord with a major third above the root - and now it is filled. {c e g}
The interval between {d} and {f} is a minor third. It does NOT sound the same, so it by itself is not a chord, but again, it is useful in a chord, so we can fill an empty chord on d, or {d a} by turning it into an {d f a}.
Whereas {g} felt to be above {c}, {e} felt to be in between.
Whereas {a} felt to be above {d}, {f} felt to be in between.
But since a major third {c C d D e} is five and a minor third {d D e f} is four, that {f} is lesser above its root than that {e}.
If {c} is in your belly and {g} is in your head, then the major third {e} is in your chest, proudly thrust forward.
If {d} is in your belly and {a} is in your head, then the minor third {f} is in your chest, retracted in shame.