Most of the time the kasra, fat7a, and Damma (the 3 short vowels i, a, and u) are not written because it's assumed that you know them (except in the Qur'aan). بارد is pronounced exactly as بارِد is, but the kasra (short i) isn't written because adults know, and also because certain letter patterns are common to them (this course will probably talk about letter patterns later). People who are learning Arabic (foreigners, children) usually use short vowels to know how it is supposed to be pronounced, and later on you get rid of them.
Honestly, that accent beneath the "r" isn't even taught to kids until they're in 5th grade. The two word is fundamentally the same in pronunciation, but the latter is grammatically incorrect. No one actually writes those accents in normal writing, only in books and the like will it be written.