Recheck your reference. I'm sure you'll find meridiem is the correct Latin term though common [mis]usage has made meridian an accepted alternate.In order to differentiate between these two 12-hour counts, we use the abbreviations a.m. and p.m. You might think that b.n. (before noon) and a.n. (after noon) would make more sense, but 17th-century Englishmen opted to use Latin instead.
In Latin, a.m. stands for "ante meridian." Translated, this means "before midday." The counterpart, p.m., stands for "post meridian," which, you guessed it, translates to "after midday."