make more common that produce
Yes, but that would be robić. Nobody ever said the sentences have to sound 100% natural in English!
Which is more common in Polish though?
I think it's difficult to compare such constructions. Someone can 'make' wine as a hobby, but that's just different from having a big company that 'produces' it.
tamto means the other
"the other" would probably be "to drugie", maaaybe "tamto" with more emphasis... that would be very context-dependent.
Why not "tamtą"?
Tamtą is for feminine nouns, but wino is neuter.
why no case (acc/gen) after the verb ?
"tamto wino" here is Accusative, but as other neuter singular nouns, it has Accusative identical to Nominative.
Same goes for masculine singular inanimate and 'not masculine-personal plural'.