Presunto vs. fiambre
The difference between presunto and fiambre depends largely on whether you are speaking European Portuguese or Brazilian Portuguese. In Portugal, there is a distinct difference based on how the meat is prepared (cured vs. cooked), whereas in Brazil, one word covers most situations.
Presunto
A1In Portugal, presunto refers specifically to dry-cured, raw ham (similar to Spanish Jamón or Italian Prosciutto); it has a dark red color and a salty flavor. In Brazil, however, presunto is the general term for the standard pink cooked ham used in sandwiches.
Em Portugal, costumamos comer melão com presunto no verão.
(In Portugal, we usually eat melon with dry-cured ham in the summer.)
Vou pedir um sanduíche de presunto e queijo na lanchonete.
(I am going to order a ham and cheese sandwich at the snack bar (Brazilian context).)
O presunto ibérico de bolota é considerado uma iguaria.
(Acorn-fed Iberian cured ham is considered a delicacy.)
Corte o presunto em fatias muito finas para servir.
(Cut the cured ham into very thin slices to serve.)
Fiambre
A2This word is used almost exclusively in Portugal (and some parts of Africa). It refers to cooked, boiled, or steam-cured ham (the pink, moist slices typically found in sandwiches). In Brazil, this word is rare and archaic; Brazilians simply use presunto for this meat.
Para o lanche da escola, fiz uma sandes de fiambre.
(For the school snack, I made a ham sandwich.)
Prefiro fiambre da perna extra porque tem menos gordura.
(I prefer extra leg ham because it has less fat.)
Podes comprar 200 gramas de fiambre no supermercado?
(Can you buy 200 grams of cooked ham at the supermarket?)
Esta pizza leva queijo, fiambre e orégãos.
(This pizza takes cheese, cooked ham, and oregano.)
Summary
To summarize: In Portugal, use presunto for salt-cured, dry ham and fiambre for cooked, pink sandwich ham. In Brazil, use presunto for the cooked sandwich ham, and specify presunto cru (raw ham) if you want the cured variety.