Diario is a periódico published all days, so almost all periódicos are diarios.
Correct. Some newspapers are dailies, others are weeklies. Some are even published more than once a day.
Why isn't "she writes for newspapers" also correct? I thought the "los" here could be a general article.
I think 'she writes for newspapers' ought to be accepted, as in English if we're talking about newspapers in general, we don't put the article. I get confused as to when Spanish sometimes puts in articles and sometimes doesn't. It is hard to tell in these isolated sentences whether we are talking about a generalisation or whether we are talking about specific newspapers.
In Spanish, unlike in English, a common-noun subject requires an article; for general statements about a subject, the subject takes a definite article. So, for example, ‘Los periódicos consumen mucho papel.’ can mean either “Newspapers consume a lot of paper.” or “The newspapers consume a lot of paper.”. A common-noun object, on the other hand, does not require an article, as in ‘Reciclamos periódicos.’ = “We recycle newspapers.”.
In both Spanish and English, the newspaper publishing industry is indicated by the definite plural ‘los periódicos’ = “the newspapers”, just like the banking industry is termed ‘los bancos’ = “the banks”.
This is not to do with subjects and objects, but to do with generalisations and specific objects.
You're right, Spanish articles work differently for objects as well, but I haven't been able to figure out the general pattern from specific examples yet…
The English term “periodicals” includes magazines and journals; the Spanish term ‘periódicos’ does not.
It's just idiomatic. Even though magazines and journals are published periodically, they're not called ‘periódicos’ in Spanish.