As the characters clearly suggest, simply refers to the big Western ocean. Not much confusion there.
, however, is an adaptation of the English "Pacific" Ocean. is a word in its own right that means roughly this: "peaceful" or "tranquil," or "pacific," if you will. According to the page linked at the bottom it had previously been known as .
It seems like may be a simplified form of , although apparently this isn't listed in all character dictionaries (note that here a person claims to have found it). The word exists and is the same word as , and based purely on shape it makes sense that one would be a . So if this theory is to be believed then the in does _not_ mean thick/fat, but rather peace as in , because simplifies to , and is not to be confused with Thailand.
Lengthy discussion about it can be found here! <