The Greek that is often translated as “testify” in English has the option of terms in Luang with different shades of meaning.
For Acts 10:42, “nala linniohora-matniohora” (“give ear-eyes about”). “This term is used when the witness actually saw the event and testifies truthfully about what he has seen.”
For Acts 10:43 and 20:24, “raltiernohora” (“talk-about”). “The focus of this term is on the talking, only without reference to the truth of the testimony. It may be used of a false witness.”
Source: Kathy Taber in Notes on Translation 1/1999, p. 9-16.