die Gans
goose
A large water bird with a long neck that is often kept as livestock.
Eine Schar Gänse landete laut schnatternd auf der Wiese am See.
A flock of geese landed on the meadow by the lake, honking loudly.

goose
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goose
A large water bird with a long neck that is often kept as livestock.
Eine Schar Gänse landete laut schnatternd auf der Wiese am See.
A flock of geese landed on the meadow by the lake, honking loudly.

The context makes clear whether the animal or the food is meant. Verbs like 'fliegen' (to fly) or 'schnattern' (to honk/chatter) point to the animal, while 'essen' (to eat), 'braten' (to roast), or 'zubereiten' (to prepare) refer to the dish.
Am Seeufer konnten wir wilde Gänse beobachten.
We were able to watch wild geese on the lakeshore.
When 'Gans' means the dish, it is often used without an article, especially in the phrase 'es gibt Gans' (there is goose / goose is being served) or as part of a compound word like 'Gänsebraten' (roast goose).
Auf der Speisekarte stand Gänsebraten mit Klößen.
Roast goose with dumplings was on the menu.
The term 'Gans' for a woman is strongly colloquial and derogatory. It should be used only with great caution, as it is perceived as an insult.
Er nannte sie eine dumme Gans, was sie sehr verletzte.
He called her a silly goose, which hurt her very much.
As an insult, 'Gans' is almost always combined with a negative adjective such as 'dumm' (stupid), 'blöd' (silly/stupid), or 'naiv' (naive).
„Du naive Gans, siehst du nicht, dass er dich anlügt?“, dachte sie.
'You naive goose, don't you see that he's lying to you?' she thought.
cow
'Kuh' and 'Gans' can both be farm animals, but they refer to very different animals. A 'Kuh' is a female bovine, while a 'Gans' is a large water bird. You might confuse them at most in the general context of farms or animal husbandry. Both words can also be used derogatorily for female people. That is rude. As an insult, 'Gans' tends to mean a naive or stupid person, while 'Kuh' sounds rougher and more strongly offensive.

Am Teich lief eine Gans langsam mit ihren Jungen durchs Gras.
By the pond, a goose slowly walked through the grass with her young.
Die Kuh lag im Schatten, während die anderen Tiere auf der Weide standen.
The cow lay in the shade while the other animals stood in the pasture.