Damasco vs. alperce
Both damasco and alperce are Portuguese nouns used to describe the apricot fruit such as Prunus armeniaca. The primary distinction between them is geographical—specifically between usage in Brazil versus Portugal—and sometimes relates to whether the fruit is fresh or dried.
Damasco
B1Damasco is the universal term used in Brazil for both the fresh and dried fruit. In Portugal, this word is used primarily in the southern regions (like the Algarve) for the fresh fruit, but it is also the standard term across the whole country when referring specifically to dried apricots.
Eu comprei uma caixa de damascos importados no supermercado.
(I bought a box of imported apricots at the supermarket.)
No Natal, nós sempre comemos damasco seco com queijo.
(At Christmas, we always eat dried apricot with cheese.)
O iogurte de damasco é muito popular no Brasil.
(Apricot yogurt is very popular in Brazil.)
Esta receita portuguesa pede damascos secos picados.
(This Portuguese recipe talks for chopped dried apricots.)
Alperce
B2Alperce is the preferred term in Central and Northern Portugal for the fresh apricot fruit. It is rarely, if ever, used in Brazil, where many speakers might not recognize the word at all.
Os alperces algarvios são doces e sumarentos.
(The apricots from the Algarve are sweet and juicy.)
O meu avô tem um alperceiro no quintal em Braga.
(My grandfather has an apricot tree in his backyard in Braga.)
Fiz uma compota de alperce caseira para o pequeno-almoço.
(I made homemade apricot jam for breakfast.)
Prefiro comer um alperce fresco do que fruta em calda.
(I prefer eating a fresh apricot rather than canned fruit.)
Summary
In summary, if you are in Brazil, always use damasco. If you are in Portugal, use alperce for the fresh fruit in the north and center, and damasco generally in the south or when referring to the dried version of the fruit.