The making of things at scale, and the environment where real users are actually served. Both mean the place where mistakes are expensive.
Latin productio (a lengthening, a bringing forth), from producere: pro- + ducere (to lead); production is the act of the same leading-forth that gives product its name, scaled up to a whole operation.
The making of things at scale, and the environment where the making is real rather than rehearsed. Both senses share the same root fact: something has been led all the way out to where it can meet other people.