They used to share an alphabet, too, but the Thai opted to simplify it (westernise it) while the Khmer opted to keep their original alphabet. Written Khmer is hard for us westerners to deal with because of this. They have lots of vowels and consonants that we don't have (I always struggle with the consonant between 'b' and 'p', because it doesn't seem like there should be any room for another consonant in there).