Just to add a bit to Faster's really good reply...
The mast is often set further back (towards the stern) on a cutter as opposed to a sloop. While some sloops are rigged with twin headsails, a true cutter's second headsail is usually set/rigged inside of the foresail (jib, genoa, etc.) and is sometimes referred to as a staysail. As you can see, the definitions and variations can get mucky. But the best advice is:
Originally Posted by Faster
In either case, if you're after that flexibility or 'look' or style, then don't sweat the definition. If you like the boat and it checks out OK... just go with it!