Translation:Today is March third.
Unfortunately, it does. There are two "main" kanji reading categories, and then some exceptions.
One is kun'yomi. These are the readings that came from the original Japanese word and matched the meaning of the kanji when they were introduced from Chinese.
Another is on'yomi. These were the readings they originally had from ancient Chinese. Since Chinese is tonal and Japanese is not, when Japanese "borrowed" these characters, many of them ended up having exactly the same pronunciation. For example, 車 kuruma can be read as sha and so can mono 者.
There's a third category(?) of kanji readings, ateji. Ateji is when a Japanese word was assigned some kanji just because they had similar sounds, even though the meanings are completely unrelated. 寿司 is one of these — apparently, that su means "natural life span" and shi means "to administer," which obviously has nothing to do with sushi.
Ateji can also refer to the opposite, i.e. kanji that was placed with an old word due to the meaning matching up, thus creating a reading that will never be used anywhere else. This is the case for these date words that trouble us so much.