The two different antigen-specific classes of cell in the immune system deal with these two different classes of parasite. B cell secrete antibodies which deal with extracellular parasites, or actually any parasite in its' extracellular phase.
T cells deal with intracellular parasites, typically viruses.
The T cell system allows the immune system to peek inside of cells where viruses are living without having to kill the cell by busting in the front door and cracking the cell open. Put rather bluntly, what goes in must go out. While the cell is a pretty good recycling system, there is inevitable left overs that have to go out in the trash. And, if the T cells were smart, they would look in the refuse for hints of visitors, or viruses. There is a large scale anonymous trash can that is generally called exocytosis and there is no way to figure if the stuff in the dump is from one house or another.