Translation:America and China
In other languages you have some countries with definite article and some without, too. Take, for example, England vs. The United States of America, or The Netherlands vs. France. I do not know if there is a rule underlying and just take it as an irregularity to learn.
I think it is, too. A lot of the countries which get "the" in English are the ones whose names are descriptions ("The Democratic Republic of the Congo", for example), but not all. For example, we say "The Lebanon" and not "Lebanon" (or we used to, at any rate: I think now it's OK to simply say "Lebanon").
My impression is that dropping the definite article shows respect. This happened to eg Ukraine. When it was called The Ukraine, it felt like an annex to Russia. Ukrainians feel more independent without the article. I'm sure there other examples, but I can't think of any at the moment.
The continent. "Continental" is the adjective. Or it could be the name of a hotel (The Continental)...
But thanks for the information, Away54. Is الأمريكتان a plural - the Americas? That's interesting, because in English we also say the Americas (see https://en.wikipedia.org/wiki/Americas ). In fact, it's probably more correct.