What are the differences between Oilskin and Dryskin?

For a short answer: Oilskin feels waxy and Dryskin feels like normal fabric. 

See a detailed explanation below:

Oilskin (also known as waxed cotton) is 100% cotton treated with paraffin waxes specially formulated to provide a surface that is water repelling & has soil removal properties. We manufacture our products in English and Australian oilskin fabric. Unlike many other oilskins, our fabric is rot-proofed and pre-shrunk resulting in a longer-lasting and more water-repelling garment.

Dryskin is a Long-lasting, breathable, water and oil-repellent fabric which looks and feels just like normal fabric. It is 100% cotton infused with a unique formulation of polymers (a type of Teflon). Dryskin can be dry-cleaned, washed in mild detergent, and ironed without decreasing its efficiency in repelling water.