I ma not sure I understand your question but generally boat with a single mast and a single sail is simply called a ''Cat'' rig. In high performance circles you also hear it called a ''Unarig''. There are a number of manufacturers who build or have built boats with this rig; Pearson, Freedom, Nonsuch and Wylie come to mind.
In Britain, a single sail catboat is called a una boat, named after a boat commissioned by the Marquis of Coyningham, built in the US and shipped to Cowes in 1853. Nothing like her had been seen before and she caused quite a sensation. Could this be what you mean?
In Cape Cod, many sailors own a single-sail 14'' catboat called a "Beetle Cat". It can be gaff or Marconi rigged. A beautiful boat, wooden,wide-beamed. Is this what you''re talking about? Contact me if you want more information on this boat.