Cyrillic vedi writes the same consonant and holds the same place, and here the numeral gap between the two alphabets opens for the first time. Glagolitic gives vede the value three, counting its own letters in order. Cyrillic gives vedi the value two, the value of Greek beta, because Cyrillic assigns numbers by the Greek alphabet and the Slavic b that stands between them takes no value at all. The offset of one that begins at this letter widens further down the order as more Slavic-only signs are skipped.
The names differ by a vowel, vede against vedi, and the difference is the kind of small variation that runs through the whole pair of alphabets. Neither form is a corruption of the other. The letter names were transmitted orally in recitation as much as in writing, and the abecedaria copied out in different centuries and different regions record them with slightly different endings, so the modern reference lists have to choose among attested forms.
Beyond the name and the sound the two letters have nothing in common. The Cyrillic sign is a Greek letter taken over almost unaltered, and the Glagolitic sign is not, which is the observation that underlies the whole question of where the Glagolitic shapes came from and why it has never been closed.