“Messiah” literally means “one who has been anointed with oil”, from Hellenistic Ancient Greek Μεσσίας (Messías), from Aramaic ܡܫܺܝܚܳܐ (məšīḥā), from Biblical Hebrew מָשִׁיחַ (māšîaḥ, “anointed”).
The Greek word “Christ” is just the literal translation of that, from Ancient Greek Χρῑστός (Khrīstós), proper noun χρῑστός (khrīstós, “[the] anointed [one]”)
Which is why some commenters have noted that the proper English translation of the name Jesus Christ would be “Oily Josh”.