These are all categorizations of different types of sailing boats. A sloop is the most common. A sloop is a monohull sailboat with a single- rig mast supporting a main sail and and headsail. These are great boats to learn sailing on as their simple, easy to handle, and have great wind performance.
A cutter at first look is similar to a sloop in that it also has a single mast positioned near the middle of the boat. However, a cutter uses two headsails, instead of a mainsail and headsail, and generally includes a bowsprit. This allows the boat to have better stability in rough weather due to the headsails providing a lower center of gravity. The complex rigging makes this boat more challenging to sail than the sloop, but provides an excellent option for an experienced sailor.
A ketch has two masts. The main mast in the front stands taller than the mizzen mast behind it. The mizzen mast stands forward of the rudder post. The ketch has smaller sails and shorter masts. While this makes them slower than a sloop, they are very controllable in rough weather which makes them excellent boats for off shore sailing.