The commonly-used galaxy classification indicates a galaxy's morphology, i.e., shape. Edwin Hubble developed the basic classification still used, the Hubble types, known collectively as the Hubble sequence:
(The term disk galaxy for a disk-like shape includes the above spiral and lenticular galaxies.) Hubble laid out the types in a Y-like diagram in the shape of a horizontal tuning fork and you do see references to the classification-structure as a tuning fork. More recent developments, generally indicated by a suffix or prefix, add more detail, often distinguishing galaxies formerly classified as "irregular". For example, the classification "SBm" is based upon the Large Magellanic Cloud's form, which does have characteristics associated with the classic barred spiral. In the less-developed system, the LMC falls under "irregular".