How does "self-contradictory" differ from "contradiction in terms"?

Sometime in college, I asked Merriam-Webster the following question. Emily Brewster replied as follows.

Q: In a recent op-ed from the Ayn Rand Institute, Onkar Ghate uses the word “self-contradictory.” In another A.R.I. op-ed, Amy Peikoff uses the phrase “contradiction in terms.”

But don’t both “self-contradictory” and “contradiction in terms” simply mean “contradictory” and “contradiction”? In other words, aren’t “self-contradictory” and “contradiction in terms” tautologous? After all, how can a contradiction be anything other than self-contradictory? And how can a contradiction be anything other than a contradiction “in terms,” i.e., if not in “terms,” then in what?

A: The terms “contradictory” and “self-contradictory” overlap in meaning. While “self-contradictory” applies only when some member or part of something contradicts some other member or part of that thing, “contradictory” applies to such conflicts both inside and outside the single item. Statements, in the plural, for example, cannot be self-contradictory, but they can be contradictory. For this reason, the term “contradictory” usually modifies plural nouns.

The words “in terms” as used in the phrase “contradiction in terms” stress that the discrepancy exists in the words being used. While I won’t rule out greater substance in some instances of the full phrase, I think “contradiction in terms” is generally equivalent to “contradiction.”