Welcome to a short introduction of the theory behind chords. You will learn how a chord is built and what separates different groups of chords.
In the cases when we only have a letter, such as C, it’s a common major chord. A major chord consists of three notes: 1st, 3rd and the 5th notes in the scale. In which scale, you may ask. In the C major scale we have:
C – D – E – F – G – A – B
So for a C major chord we can locate the 1st, 3rd and 5th as C, E and G.
Sometimes we find chords with names such as Cm, Dm, Em. The “m” stands for minor and in a minor chord we have three notes: 1st, 3rd minor and 5th. The notes in Cm are C, Eb (E flat) and G.
You may ask how it comes that we only have three notes in a C major chord when you have learned to strum five strings playing this chord:
C major chord
The reason is the instrument. The notes are ordered less symmetrical on the guitars fretboard opposed to the piano keyboard. Another reason is that musical context differs from piano to guitar: you cannot play the harmony with your left hand and the melody with your right hand simultaneously on the guitar. Therefore, we don’t need to worry about too many notes being played at the same time.
As you can see in the diagram above, there're five notes played together in a C major chord: C, E, G (open string), C and E (open string). It's the most practical way to play the open C chord. In chords, we often find numbers after the letters: C5, C7, and C9 to list a few. In a C5 chord (also called power chord), we only have two notes: the 1st and the 5th. That's pretty unproblematic. Therefore, the C5 consist of C and G.
In the case of the seven, things are little messier. First of all: there’s C7, Cm7 and Cmaj7. C7 is called the dominant 7th. A C7 consists of the C major chord plus the flat 7th. In a C scale the flat 7th is Bb (B flat). In a Cm7 chord we add the flat 7th to a C minor chord. Finally, in a Cmaj7 chord we add the major 7th to a C major chord.
You may wonder what actually differ between chords like C9 and Cadd9 or C13 and Cmaj13. Here you got the answers in a tone perspective:
The difference between 9th and add9 is the flattened 7th.
C9: C, E, G, Bb, D
Cadd9: C, E, G, D
In other words, the 9th chord includes all the tones in a 7th chord, but is extended with a ninth.
The difference between 9th and 7(#9) is a raised ninth
C9: C, E, G, Bb, D
C7(#9): C, E, G, Bb, D#
C7(#9) is an altered ninth chord, quite uncommon, but it's not impossible you will encounter it.
The difference between 13th and 13 major is a flattened and a natural 7th.
C13: C, E, G, Bb, D, A
Cmaj13: C, E, G, B, D, A
When you memorize this you are helped by thinking about the 7th versus maj7 and when add two note to each chord (13th and 13maj).
On this site you find lots of other chords like sus chords and slash chords. These chords have special sections and are explained together with its theory there as well. You could get supplementary knowledge by reading What is a guitar chord?.
For more in depth reading, see:
Music Theory for Guitarists: Everything You Ever Wanted to Know But Were Afraid to Ask
Music Theory 1 & 2 Basic Chords and Extended Chords Color Chord Tones
The connections of chords
Some chords are connected to each other in the way the notes belong to the same scale. For example:
C - Dm - Em - F- G - Am - Bdim
These seven chords have notes that all belongs to the C major scale. Try to play some of them in different order and you can hear they fit well together.
The same thing could be done with four notes chord types:
Cmaj7 - Dm7 - Em7 - Fmaj7- G7 - Am7 - Bm7b5
Once again, all these chords have notes that belong to the C major and once again you could play them and hear that they fit well together.
See the Chart with chords sorted by key for different keys.