The letters were made in a mission and the alphabet was finished in a state, and the difference between those two settings is carried by the two literary schools of the First Bulgarian Empire.
At Ohrid, in the south west of the empire, Clement and Naum, pupils of the Thessalonican brothers, ran a school that trained clergy in very large numbers and continued to work in Glagolitic, the alphabet their teachers had made. Its output was pastoral: the texts a working priest needed, in the script the mission had used.
At Preslav, the capital, a school worked under the patronage of the ruler and produced translation, compilation and original composition on a court scale. The alphabet now called Cyrillic is generally held to have been assembled here, in an environment where Greek books, Greek scribes and Greek administrative habits were close at hand, and where a script that looked Greek carried an argument about the standing of the Bulgarian church.
The relationship between the two is regularly flattened into a sequence. It was not one. The schools overlapped in time, and both scripts were in use, in some places on the same page, for generations. A late source attributes the invention of letters to Clement himself, and the claim is argued rather than accepted: it may be a memory of his work on the alphabet, or a later attempt to give the newer script the older school as a parent.
What is not in dispute is that neither school was working alone, and that Cyrillic was an institutional product rather than one person's invention.