No. Everywhere uses the same terms, you just didn’t understand the question.
The result of addition is the sum. The sum is calculated by summation of inputs.
The result of multiplication is the product. The product is calculated by __________ of inputs.
OP’s question is: why can’t the blank be “production”, by analogy with “summation”?
I think that’s probably a fairly uncontroversial opinion. In the city-builder genre, Lethis: Path of Progress aimed to be the definitive city-building game of its time, hoping to match the peaks of Caesar and Pharaoh in the city-builder heyday. Instead, Lethis ended up being a huge flop, precisely because it slavishly copied the mechanics of Caesar without understanding that games as a whole have evolved since then.
Lethis lacked certain quality of life features that now feel obvious and baseline. What’s sad is that these features had already evolved towards the tail end of the city-builder heyday, in games such as Children of the Nile, and now feel glaringly obvious by their omission. Other city-builders that haven’t been so tied to the classics have seen more success (although there’s been no true breakout hits, sadly, no great renaissance in the genre).