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”?

“Summation” already means something else, and funnily enough words can have different meanings in different contexts without causing any confusion.

OP literally emphasised the distinction between process and result in their post, specifically so that this exact confusion would not occur, and yet still everyone is talking about the word for the result instead of the process.

I never cease to be baffled by the seemingly boundless glee with which Americans will repeat this myth that has no basis outside of Internet cope. Literally nobody born in the last 100 years would read “trump” to mean “fart”. The only meaning of “trump” to British people is the winning suit in a game of cards, or the concept of winning in general. There’s literally a collectible card game in Britain called “Top Trumps”, and let me tell you, it ain’t about huffing farts. Unlike your absurd comment.

And even if people did understand “trump” to mean “fart”, it’s still an astonishing feat of mental gymnastics to claim that “it makes no sense that you would elect someone called that”, because funnily enough, a person’s name is totally unrelated to their ability to do the job, and lots of people have funny-sounding names that go completely unremarked upon, because people understand that a name is just a name.

I absolutely hate the guy, and yet when I see people purporting to make fun of his name based on something that isn’t even true, rather than, y’know, attacking his actual policies and actions, it makes me despair at the pathetic state of American politics. Seriously, your country is going to the dogs, and the best thing you could think of to combat that is to baselessly make fun of a guy’s name?