As our colleague from Scotland explained the root biotrophic means live feeding from the Greek. These parasites feed off of living cells. Necrotrophic or literally dead feeding is those parasites living off of cells that are first killed. In relation biotrophic fungi like rusts and powdery mildew they are obligate parasites signifying need for a live host plant. Necrotrophic parasites live as saprophytes and can usually grow on laboratory culture media. Obligate parasites have intracellular nutrient exchange sites can haustoria. In necrotrophic feeding toxins and enzymes can kill the cells before they are utilized for sustenance.
This link above will help you. This link contains the definitions and differences between biotrophic and necrotrophic fungi.
Biotrophic pathogens - pathogens that obtain food only from living host cells
Necrotrophic pathogens - They kill the host before invading it, it maintains a saprophytic activity, with nutrient withdraw of dead cells. These pathogens are characterized by intense enzymatic and toxicogenic activity