At least in US agriculture, when they speak of productivity they generally refer to pounds per acre for crops. For livestock it's a bit less clear, they sometimes refer to pounds of feed to final live weight. You generally have to schedule a slaughter day months out and you estimate the final weight, you don't get paid as well if you are too far off the weight in either direction. Its less common generally, but in the cattle industry I've heard the accuracy of hitting that targets talked about as productivity.

I agree with you on the double speak though, really I think its just a lack of the public really understanding the meaning given to "productive" in the industry though. The industry doesn't hide what it means by the word, most just don't care about any version of productive that measures things like nutrient value, sustainability, soil health, animal welfare, etc.