to say: to state something in words, especially to report what a person said in reply
This is one of the New Testament's plain verbs for speaking, and almost always it simply reports what someone said. It turns up most often in the storyteller's voice, introducing a reply: Jesus "said" to the tempter, the centurion "said" he was not worthy, Pilate "said" he found no fault. The past-tense form behind "he said" is the one you meet again and again in the Gospels and Acts.
The same verb does a second, quieter job when a writer steps in to pin down his own point. Here the sense slides from bare reporting toward "I mean" or "what I am saying is this." Paul uses it this way when he pauses an argument to state plainly what he is and is not claiming. The word has not changed its meaning, only its angle: instead of relaying someone else's words it underlines the speaker's own.
Because it is so ordinary, the choice between "he said," "he replied," "he declared," or "he affirmed" in English is a matter of the surrounding scene, not of any extra force packed into the word itself.