Harmonium: reeds; blown; single, double manual; foot or hand blown.

American Organ: reeds; suction; single, double manual; foot or
hand blown.

Either of the above might also come with a pedal board.

Church Organ could be: Pipes, wooden, metal or a mixture,
hand-played or roll/barrel played; (hand-turned or foot-blown
or electric blower).

Bird organ/Serinette: a small 10-note pipe organ, played with
a pinned barrel, 1780's, to teach birds to sing.  Sometimes
2 ranks, wooden or metal pipes, high pitched.

Organettes: Reeds of steel, alloy or brass; suction or blowing;
  Over 565 different types discovered so far, playing 192 types
  of music:
    paper/card strips/loops/rolls
    card/metal discs with slots/projections (several types)
    card book music, metal plates, barrels, cobs.
  Single/double/triple reeds per note (double reeds are tuned
  Celeste or octave)
  Hand-turned or foot pumped, sometimes mouth-blown.

Fair-Organs: large fully automated with and without lighting
  effects; played by music book or rolls; high pressure for
  long distance sound exposure.

Band Organs: U.S.A. term for Fair-Organ which is used in Europe.

Dance Organ: like the fair organ but quieter voicing for indoor use.

Street Organ: hand-turned; moved around by one person;
  pipes or reeds; roll, book, barrel or computer chip operated.

Street Barrel Piano : (often wrongly called Barrel Organ following
broadcasting on BBC in 1950's here in UK by Cannon Wintle).

Automatic Pipe Organs also include roll playing attachments to
Wurlitzer Cinema Organs, Aeolian Residence Organs (58/116/176 hole
rolls), Dumb-Organist playing unit (mostly church use).

The more I think about this, the longer the list gets!
A family tree would be interesting!

Kevin McElhone, Northampton, UK