As nouns the difference between anchorite and ascetic
is that
anchorite is one who lives in isolation or seclusion, especially for religious reasons while
ascetic is one who is devoted to the practice of self-denial, either through seclusion or stringent abstinence.
As an adjective ascetic is
of or relating to ascetics; characterized by rigorous self-denial or self-discipline; austere; abstinent; involving a withholding of physical pleasure.