Learn English – Difference between “mark” and “marker”

I'm afraid that there is no definite answer, since both roles are pure fiction and their attributes may change as in role playing games they have a difference (different spells and skills). Only the etymology could give a clue

From etymonline

sorcerer 1520s, earlier sorcer, from O.Fr. sorcier (see sorcery). Sorcerer’s apprentice was a symphonic poem by Paul Dukas (1897) based on a Goethe ballad ("Der Zauberlehrling," 1797), but the common figurative use of the term (1952) comes after Disney’s “Fantasia” (1940).

wizard mid-15c., "philosopher, sage," from M.E. wys "wise" (see wise (adj.)) + -ard. Cf. Lith. zynyste "magic," zynys "sorcerer," zyne "witch," all from zinoti "to know." The ground sense is perhaps "to know the future." The meaning "one with magical power" did not emerge distinctly until c.1550, the distinction between philosophy and magic being blurred in the Middle Ages. As a slang word meaning "excellent" it is recorded from 1922.

If you are accountable for something, you are in a position that requires you to report to or answer to someone for your actions and decisions.

If you are responsible for something, you may be the one to whom things are reported.

I think with accountability there is someone or some agency overseeing your actions; someone to whom you report.

With responsibility, you are the one in charge. "The buck stops here." One dictionary says when you are responsible, you have the ability to act without guidance or superior authority.