I agree with you. I teach paradoxes as sentences and oxymorons as word pairs, but I think the differences may be negligible. They are part of the same branch of equivocal language. All oxymorons are paradoxical, but not paradoxes are oxymorons. Most oxymorons are words or phrases; all paradoxes are statements. A paradox is generally more absurd and counterintuitive, while an oxymoron is more poetically obvious and cutesy.
Enotes says this:
Oxymoron - a figure of speech in which two contradictory words or phrases are combined to produce a rhetorical effect by means of a concise paradox.
...In Shakespeare’s Sonnet 142, the speaker declares:
“Love is my sin, and thy dear virtue hate.”
The above statement is a paradox, and within it has an oxymoron "virtue hate."
I teach "Foul is fair and fair is foul" as paradox, not oxymoron. Shakespeare usually pairs his oxymorons, like in Romeo and Juliet, when Romeo says "cold fire," "feather of lead" etc...
As was mentioned in the previous post, an oxymoron is a figure of speech where two contradictory or opposite words are combined to create a dramatic effect. In addition to the dramatic effect, oxymorons also make the audience stop to think in order to laugh or further contemplate a certain idea. A paradox is similar to an oxymoron in that it is a contradictory statement, but it is expressed in a sentence or group of sentences and contains an implied truth. In Act Two, Scene 3, Macduff uses the oxymoron "joyful trouble" to describe how hosting King Duncan is both an honor and pain. In Act Three, Scene 6, Lennox also uses the oxymoron "pious rage" to describe Macbeth's brutal actions. Supposedly, Macbeth murdered King Duncan's two chamberlains after he discovered that they killed the king. In Lennox's opinion, Macbeth was acting pious, in that he was genuine and virtuous, while he proceeded to kill the chamberlains out of rage. Macbeth's rage was essentially justified because he felt it was necessary to revenge the king's murder.