I arrived first - eu fui o primeiro a chegar.
I was the first to arrive - eu cheguei primeiro
(eu fui o primeiro a chegar, no trabalho no local da cena, do acidente etc).
When we used to sell the fish to traders in our village, the fisherman who arrived first were given good prices, but to those who came later were paid the price they wanted to give.
Quando nós vendíamos o peixe para nosso próprio vilarejo, o pescador que chegasse primeiro, nós comerciantes davamos um bom preço, mas aos que chegassem depois lhes era dado o preço que quisessem.
During the conference, it was evident that Argentina is always the first country to arrive bringing aid.
Porque vimos, durante a conferência, que a Argentina é o primeiro país que sempre chega para levar ajuda.
In the first case WHOEVER came first, in the second case it means the very first one, the pioneer, or "when we want to emphasize" that someone came to a place before all the others.
In Portuguese, one could translate "o primeiro a chegar" in both senses (with the two possible meanings), the situation would tip the scale here (would define which one in English).