Bar chords are probably the most common example of moveable chord shapes. However, any chord which does not contain open strings can be moved to any position on the fretboard. Most moveable chord shapes follow the five basic forms found in open chords, i.e. Q A, G, E and D. Because Root Six Bar chords follow the basic shape of an open E chord, they can be described as E form chords. Root Five Bar chords follow the basic shape of an A chord, so they can be described as A form chords.
Root Four chords do not necessarily require a Bar, because the first finger can be used singularly on $, thereby leaving 2, 3 and 4 to finger the treble strings.
Root Four chords follow the basic shape of a D chord so they can be described as D form chords.