As already mentioned in the introductory chapter the indefinite article is used if a noun doesn't possess any individuality. It resembles a little bit to adjectives indefinita like any, although any stresses the arbitrarity.
1) I am looking for a job.
2) I am looking for any job.
In both cases he has only a vague idea what he wants to do, but in 2) he definitively doesn't care with what he earns a living. That goes in the same direction as 1), but in 2) the arbitrarity is the central message.
It is possible that in certain contexts the use of the definitive article in English differs from its use in Portuguese, but in general there is no difference. The main difference consists in the form. The english definitive article doesn't distinguish between masculine and feminine and there is no plural form. If we need it in plural, we use some, a completely different word.
This said, there is a little difference. The um portugues is a number as well, in this case it would be one in english. Therefore um is ambiguous. The meaning can be just any or one.
1) Tem um carro. => He has one car. / He has a car.
2) Um homem cruza a rua. => One man crosses the street. / A man crosses the street.
There exists therefore a difference in theory, although we can always deduce from the context the meaning.
In general we can say that if there is no undefinite article in English, there is none in Portuguese as well. This is for instance the case if we refere to the totality of something, to the specie, to the whole.
Cakes taste well. => all the cakes
The cake tastes well. => one cake
Some cakes taste well. => part of the cakes
Many people ask whether it is possible to explore the city without car.
In some regions people with a beard are considered important.