Our translation follows the theory that most ‘New Testament’ books were originally in Aramaic (except for Mark, Luke, and Acts). In that language, the word used for ‘crucify’ is a verb meaning to make erect, or to be lifted up, or raised up.
It’s somewhat like our English word ‘hang’ or ‘hung,’ where it means more than just being hung like a picture on a wall – the cultural context of the word really means executed by means of hanging from the neck.
It’s the same in Aramaic. Being ‘raised up,’ in the right context, actually means to be executed by means of being raised up onto a (usually cross-shaped) piece of lumber. So, to save time and to be brief, in many places our translation just says executed.