"She has a big stomach."
Translation:Ona ma duży brzuch.
Technically perhaps, but in fact "stomach" has both meanings, and is used in this context more often than "belly", which often has negative connotations, for example "beer belly". Unless someone is pregnant maybe.
Check "big stomach" at Google images and you'll see lots of bellies, but not so many medical diagrams.
So "can be", but not "should be".
I can partially agree with you. Yes, the word 'stomach' can be used when referring to the abdomen, although you will seldom hear a native speaker saying "Oh! Your stomach is so flat/looks impressive!" or "Your stomach is so big". Stomach is an organ which stores and digests food. As I have mentioned, it can be used when referring to the abdomen, but it is a term reserved for more formal situations, such as visiting a doctor - 'my stomach aches'. Belly/Tum/Tummy are proper equivalents of Polish "brzuch", and these are used in a casual, everyday speech by NSs. There is a reason why 'belly button' is an informal version of 'the naval' - 'stomach button' would sound comical. To be honest, it is not the 'belly' but 'tummy' that is probably the most frequently used term when referring to the area between the legs and the chest, i.e. the abdomen, since 'belly', as you have already mentioned, may carry some negative connotations. Finally, the use of 'stomach' in all kinds of contexts is often advocated by teachers of English as a second language - and that is a real problem.
Ah and I do not consider 'Google images' as a reliable source of knowledge ;)
Well I'm both a native speaker (BrE) and also plead guilty to being an EFL teacher. I don't discount "tummy", although I'd say it's more used within the family and with close friends (listed in Oxford as "informal"). As for your example, I don't know many people who go round telling people other than family and close friends that their whatever looks impressive, so I'm afraid for me that's not a real clincher.
The normal word used among adults who aren't close friends or family I would imagine to be "stomach", and it's certainly the word I'd use in the office, for example. But that's not really the issue here.
My point is that in the vast majority of cases we use "stomach" to mean "brzuch" rather than "żołądek", and for me at least, it sounds better here than "belly" or "abdomen". What's more, this meaning is listed in standard dictionaries, which perhaps you might find more reliable:
"1.3 The front part of the body between the chest and thighs; the belly.
‘Blake hit him in the stomach’ "
"c : the part of the body that contains the stomach : belly, abdomen
He was punched in the stomach"