On the piano
The keyboard shows the same three notes as a shape you can see. The coloured keys are the C major arpeggio, the pale keys are the rest of C major, and you can click any key to hear it.
On the staff
On a treble staff, C is written C, E and G.
The staff shows the notes one after the other, then together. Written this way the chord is in close position, which means each note sits as near to the one below it as the spelling allows. A guitar almost never plays a chord in close position.
C under a hand
Strummed from the lowest string to the highest, this grip sounds C, G, C, E, G and C, which are the degrees 1 5 1 3 5 1 rather than the 1 3 5 of the written chord. The root is the lowest note, so this grip is in root position and sounds the way the written chord suggests. With C in the bass and six strings sounding three notes, the 1 and 5 appear more than once.
Strummed from the lowest string to the highest, this grip sounds E, C, E, G, C and E, which are the degrees 3 1 3 5 1 3 rather than the 1 3 5 of the written chord. The lowest note is the 3 rather than the root, so this grip is in first inversion, written C/E. It has the same notes as the root-position grip, but with E in the bass it sounds different. With E in the bass and six strings sounding three notes, the 1 and 3 appear more than once.
Strummed from the lowest string to the highest, this grip sounds G, C, G, C, E and G, which are the degrees 5 1 5 1 3 5 rather than the 1 3 5 of the written chord. The lowest note is the 5 rather than the root, so this grip is in second inversion, written C/G. It has the same notes as the root-position grip, but with G in the bass it sounds different. With G in the bass and six strings sounding three notes, the 1 and 5 appear more than once.
Three shapes for C on guitar: C, C/E and C/G.
Every grip here is C, but no two of them sound alike. A chord with the root as its lowest note is in root position, and a chord with any other note at the bottom is an inversion. On a keyboard you choose the inversion you want, but on a neck the shape your hand can reach usually decides it for you. When a grip sounds a note more than once, the fretting hand decides which note that is, not the harmony.
A triad is a chord of three notes, and building one takes only two decisions. Take a root, stack a third on it, and then stack another third on top of that. C, E and G are a major third followed by a minor third, which makes a major chord.
If you reverse the order of the two thirds, the chord becomes minor: C, E♭ and G. The outer interval is a perfect fifth in both cases, so the only difference between major and minor is the note in the middle. The root and the fifth stay the same.
On a keyboard, a triad is three keys. On a guitar it is three notes spread across six strings, and the next lesson explains what the extra strings do.