In the section on Chords using 4ths, you learned a chord shape using 4th intervals which has more than one name. This is true of many chords. The name of a chord often depends on the context in which it is used. For example, the notes E, G and B make up an E minor triad. If you see an Em chord symbol, you can simply play any fingering of an E minor chord.
However, if the bass plays a C note under this chord, the effect of a Cmaj7 chord is created. E, G and B are then functioning as the 3rd, 5th and 7th of the chords. This means you could play an E minor triad anywhere you see a Cmaj7 chord symbol. This is an example of scale tone substitution, which is explained on here .
Most slash chords also add up to another chord type. Sometimes it makes more sense to describe the chord as a slash chord, (e.g., when a pedal tone is being used) and other times it makes more sense to describe the chord as what the notes add up to. Here is an example featuring the slash chord D/C. Its notes are D, F# and A over a C bass note.
If you analyze the chord D/C, you will find that the notes add up to a D7 chord - C is the flattened 7th degree. This means the same chord could also be described as a 3rd inversion D7 chord. Here is an example using the chord in this way.
Another possible use for the same group of notes is as a C13#11 chord. The C note is the root of the chord, the D note functions as the 9th degree of the chord, the F#11 is the #11 and the A is the 13th. Try the following progression using the same chord voicing as the D7 from the previous example. Notice how the context completely alters the effect of the chord.