What is the name for the linguistic concept?

Absence of evidence is not evidence of absence.

What is right is not always popular, what is popular is not always right.

and in the negative;

We park in driveways, and drive in parkways.
Is there a term for pairings of this type?

Antimetabole.

My suggestion: Chiasmus.

No, not a chiasmus. Here’s a chiasmus:

The heavens are telling the glory of God;
the wonder of his works displays the firmament.

subject-verb-object
object-verb-subject

Note the third-person singular verb in the second sentence: it’s “the firmament displays the wonder of his works” as an echo of “the heavens are telling the glory of God”, but the sentence structure has been inverted for poetic effect. So there’s a structural “cross-over” between the two sentences.

It is indeed Antimetabole.

I googled it… and the Abscense of Evidence came up.

Thanks gang

Actually, wonder and firmament are both nouns in the singular. Perhaps the wonders of his works displays the firmament would work better as an example?