I answer my own question. Satu surat kabar/Satu koran = One newspaper. Sebuah surat kabar/Sebuah koran = A newspaper.
Kabar = new. So newspaper, literally: letter/mail with news (inside) = newspaper.
The English is literally a paper with news (inside), so it's almost the same. It is often used only "paper" as a short word for "newspaper".
For the "koran" meaning. It is from a French name "courant", it also gave the English word "current".