What's the difference between 海獣 and 怪獣? Do they both mean the same thing, or is one proper and the other one not?
怪獣【かいじゅう】 is a common word that refers to (big) monsters. This was a popular genre in the Japanese film industry, and there is an Wikipedia article written in English. Character-wise, 怪 means "wicked; strange", and 獣 means "beast; monster".
海獣【かいじゅう】 is a rare biological term which refers to marine mammals such as seals, whales and manatees. The kanji 海 means "sea; ocean". This word is normally used in academic contexts, so usually there is no chance of confusion. But in some fictional works, it may be also used to refer to "marine monsters" such as Kraken.