Equivocation
Etymology
From Late Latin "aequivocatio," from "aequus," "equal," and "vox," "voice" or "word" — hence "equal-voiced," a single word carrying more than one sense. As a named fallacy it describes an argument that stays valid only because a key term means one thing in the premise and another in the conclusion. In everyday use it also covers the deliberate vagueness people use to dodge a straight answer.
noun · /ih-kwiv-uh-KAY-shun/
The use of ambiguous language, especially a single term shifting meaning, to mislead or avoid commitment.
What it names
The slippery move where one word does two jobs — letting a speaker seem to prove something by trading on a meaning they quietly swapped mid-argument.
Example
His denial was a careful equivocation: true on one reading of "involved," and false on the one everyone assumed.
Related idea
Equivocation exploits a genuine ambiguity in words; broader sophistry includes any clever fallacy, of which equivocation is one especially common trick.