> parachute nylon
This describes the application, not the fabric.
> taffeta nylon
> oxford nylon
Subtle differences in the weaving process, often used to fool the consumer in marketing literature. The terms can be misapplied too.
A genuine plain weave is usually finer than a taffeta, which is often (as far as I can tell) done with an air-jet loom. A plain weave is often slightly dearer. Oxford usually applies to heavier fabrics.