Simplist way to define this. A cutlass is a cutlass, a rapier is a rapier, a longsword is a longsword and a shortsword is a shortsword - basically these are four different bladed weapons. While all bladed weapons have some similarities, only the rapier even resembles a cutlass (both being single edged, one-handed weapons), with the other two being double edged weapons. I've seen real cutlasses that were much longer than what the PF cutlass is supposed to be, but I don't know if these is a specific parameter in length or weight that defines what is a cutlass and what is not. According to PF a cutlass is a shorter weapon that is easily wielded aboard ship, so likely not comparable to a long sword. Ideally, I'd say these are four different weapons, though rapier is most similar to a cutlass.
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