Well.... not always.... the milk is azedo meaning it's spoiled. But azedo also refers to things like lemon. Amargo would be bitter, not used for spoiled things, but for things which have no much sugar. We say the coffee is amargo (little sugar) not using azedo, since it doesnt "get spoiled". For strong beverages we also say amargo. Vodka é uma bebida amarga.
from a dictionary: AZEDO: sourness, acidity, acidness. adj 1 sour, tart, tartish, sharp, acid. 2 rough, harsh; AMARGO: 1 bitter (quality or taste). 2 (bras) tea without sugar. 3 (bras) amargos bitter remedies. adj bitter: a) acrid, acrimonous. b) distressing, painful, sad. c) hard to bear. d) harsh, severe (complaints, words). e) fig sour, sardonic. até o amargo fim to the bitter end.