I see a few different descriptions in this thread! Here's my take:
Cats
Shallow-water catamaran - These are the cats mostly talked about in this forum. They are not "true" catamarans, but more like full tunnels on steroids, or an oversized tunnel built into a monohull-type boat. They run very shallow on plane, and have a decent ride in the chop, but they will draft more than a similar monohull when at rest.
True catamaran - These are boats that are comprised of two separate hulls (and often an engine on each hull). They are displacement, or semi-displacement, vessels that can typically draft four feet or more. These cats can offer a comfortable ride in bigger waves and often found offshore. You'll see a lot of these in the South Pacific.
Tunnels
Full-tunnel - these are somewhat similar to the shallow-water cats described above, but also describe the full-tunnel race boats - those little boats that are designed to go over 100mph and do nothing else. Those boats effectively use the ram air lift in the tunnel to help with lessening draft and getting more speed (I really don't think the air lift provides a significant benefit below 50mph or so).
Short or mid-tunnel (sometimes called marsh tunnels) - these are the tunnels common to the flats boats discussed on this forum. They usually stretch across the rear third or half of the boat and receive no air ingestion from the bow. Some of the tunnels may be shorter, maybe one-quarter the length of the boat or less, but I don't think they perform as well. It takes a lot of science and good engineering to make a good tunnel, and I think there remains plenty of room for improvement in this area.
Pocket tunnel - these are really short tunnels found on a few bay boats. I'm not really sure what their advantage is...maybe getting the engine a little shallower when putting around, but their design seems inefficient for good water feed to the prop when on plane. In some cases, they may act like a stepped boat hull to allow the engine to run a little higher, but still an inefficient water feed in my mind.