SS Cyril and Methodius invented the Glagolitic alphabet (something akin to the gruzian or Georgian alphabet) that had absolutely no similarity to anything Greek or Roman.
Glagolitic Alphabet. Glagol in Old Slavonic means word
The Cyrillic alphabet was invented by one of St. Cyrill's disciples (I forget his name), who named it in honor of his teacher.
Vast majority of Cyrillic is Greek.
Cyrillic alphabet (Russian version)
Greek letters in the Cyrillic alphabet are A, V, G, D, E, Z, I/J, K, L, M, N*, O, P, R, S**, T, U, F, and H.
*Cyrillic N looks like H, but it was originally derived from the Greek N, which looks like N.
**The S, written as C, is a variant of Greek sigma (as abbreviate don icons IC XR)
Strictly Slavic letters are zh, ch, ts,, soft and hard signs (yeri and yer), yu, ya, yi, and ye.
The original Church Salvonic Cyrillic had more Greek letters such as izhitsa, and threta, as wlel as omega.
Later on different nations added their own letters.