There are two types of English relative clause. Their traditional names are defining (or restrictive) and non-defining (or non-restrictive). ‘The Cambridge Grammar of the English Language’ uses the terms integrated and supplementary, which seem to me to explain their difference more clearly. Integrated relative clauses are essential to the meaning of a sentence and cannot be omitted if the meaning is to be retained. Supplementary relative clauses provide additional information. When a supplementary relative clause is removed, a sentence with the same underlying meaning remains.
It is the convention to set off supplementary relative clauses with commas, so that if your first example had included a supplementary relative clause it would have appeared as ‘My sister, who is from Chicago, visited me last weekend.’ That would have left little doubt that you had only one sister. Without commas, the clause ‘who is from Chicago’ becomes an integrated relative clause and leaves the reader with the strong impression that you have more than one sister but that the one who visited you last week-end is from Chicago.
The sentence ‘The car that I bought last week is red’ contains the integrated clause ‘that I bought last week’. It tells us that of all the possible cars you could be talking about you are talking about only one, that is, the one you bought last week. The sentence about your aunt who is from Chicago doesn’t deny the possibility that there might be other aunts elsewhere. Similarly, the sentence about the car you bought last week doesn’t deny the possibility that there might be other cars elsewhere. You aren’t contrasting the car you bought with any other cars you may already own, but with all the other cars in the world. If we were to treat the clause as supplementary and write ‘The car, that I bought last week, is red’ we could remove the clause and be left with ‘The car is red’ and that would be a grammatical sentence. But it conveys different information, lacking as it does the crucial point about which particular car you’re talking about, that is, the one you bought last week.