"제가 책을 빌려요."
Translation:I borrow a book.
Same here. English isn't my native language, though. So is "borrow" and "rent" a different concept both in Korean and English? Usually, borrow is used in the context where we can lend something for free, like "I borrow her book." Which usually without charge. Yet if we say "I rent a book", I automatically think that this person has to pay a sum of money in order to borrow this book. Do I make any sense? I'm a bit confused here.
Very possible. It is claimed that 빌려 or 빌리어 might have come from the Old English "borg" meaning "pledge, security, bail, debt".
"Sense shifted in Old English to the modern one, "take or obtain (something) on pledge to return it or security given," apparently on the notion of collateral deposited as security for something borrowed." (i.e. to borrow). [@etymonline]