I guess conventional materials are the commonly used materials for a specific application.  Advanced materials have to be new or at least better modified old materials but  not yet popular. 

It's up to the beholder

The classification is arbitrary based on particular time period in history. For example, BC 4000, Copper and brass were advanced materials, AD 1900 Aluminum was an advanced material, AD 1920 Stainless Steel was an advanced material. When existing materials fail or do not satisfy the functional requirements, new materials are developed. Those new materials are known as Advanced Materials. As time proceeds, this category of Advanced Materials would become Conventional Materials. Considering the time period in which we live and the question is asked, I will say the following materials can be treated as Advanced Material in the realm of Mechanical Engineering. All composite materials (Polymer, Metal, Ceramic  Matrix Composites) , super alloys, new generation steels such as HSLA, ODS, IF etc., high entropy alloys, Carbon Nano Tubes etc.