There is no serious difference between the two words. Each came from the Latin Græcia with one trail keeping the Latin “c” in spelling, but conforming to English pronunciation rules for “c followed by i or e” and the other following the Latin pronunciation and adopting the “k” to keep the pronunciation consistent. Until (I believe) the 16th century, the word “Greekish” supplied the same meanings.
In usage, Grecian has come to be used to mean “in the style of the Greeks” while “Greek” continues to handle the rest of the adjectival forms. However, that is a connotative value and aside from sounding a bit odd, it is not incorrect to refer to “Greek” objects or actions as “Grecian.”