>The minstrel show, or minstrelsy, was an American form of entertainment developed in the early 19th century. Each show consisted of comic skits, variety acts, dancing, and music performances that mocked people specifically of African descent. The shows were performed by white people in make-up or blackface for the purpose of playing the role of black people.
They aren't the same thing: minstrelsy is the root offensive thing, blackface is offensive by association with minstrelsy. “Nerd blackface” could be any instance of non-nerds portraying nerds [0], “nerd minstrelsy” would, at least if you take the modern objection as defining [1], be the unfavorable portrayal of nerds (whether by actual nerds or non-nerds) for the entertainment of non-nerds.
[0] which is problematic as a blanket characterization of TBBT, though it may apply to some players; it seems pretty clearly not to apply to Dr. Bialik, for instance.
[1] historically, from some quarters it was roundly attacked on the opposite basis, for excessively sympathetic portrayal of blacks, especially during slavery, and especially for it's frequent positive (from the viewpoint of those objecting) portrayal of runaway slaves.
