Both has strong ties to ancient Greek, probably based on it, but different. Ukrainian and Russian has more in common than both of it with a Greek separately. Pre-1917 Russian employed some Latin letters as well as extra original letters, similar to Ukrainian, but it was all eliminated by Bolshevik language reform.
The Cyrillic alphabet was developed by two monks Cyril and Methody The Kievan Rus had ties with Byzantium and many letters are Greek, alpha beta gamma lambda rho tau mu nu etc for sounds that they needed new letters for sha za ya they created them
Interestingly Ukrainian language has its roots in the Czech language not Russian. When well spoken it is very light and almost musical