Bi'l-taḥqīq requires attention to a word's genuinely assigned sense. Bi'l-taʾwīl permits a rhetorical claim that an external subject belongs to the class represented by that sense.
رأيت أسداً يخطب
I saw a lion delivering a sermon.
The verb “delivering a sermon” supplies a clue to a human orator. “Lion” has not acquired a new zoological sense meaning “human preacher.” Rather, courage is expressed through the imaginative claim that the orator belongs to the category of lions.