The algae or bacteria live inside the fungus, and exchange nutrients with it. Lichens pose a problem for biological classification, because the three types of organism concerned come from three different kingdoms.
This allows specimens to be put into boxes and labelled.
By having specific names, researchers know what they are working on: that is one of the basic functions of taxonomy. In those fungi which may associate either with an alga, or with a cyanobacterium, the resulting forms (called photomorphs) may look quite different, yet are now referred to by the same name.
Most common (over 40%) are Ascomycetes, which produce spores in a sac-shaped container, the ascus.
Only a few types of alga occur within lichens; these algae also have their own names.
Nor, since they will refuse to rush a decision, will they succumb to high-pressure tactics themselves.