Austenitic and martensitic describe the microstructure of the steel - the crystalline structure at atomic level - and that microstructure sets many of the mechanical and physical properties.
Austenitic stainless steels have relatively modest strength but good impact properties. They are easier to form and weld, are non-magnetic, and offer a range of good to excellent corrosion resistance.
Martensitic stainless steels are the opposite in most respects. They have very high strength but lower impact properties, are more difficult to form and weld, are magnetic, and have a lower level of corrosion resistance. Their lower alloy content can make them lower cost, depending on the condition supplied.