One possibility is that the spelling of the name got changed somewhere/some time, while the arms remained unchanged. (I've an instance of this sort of spelling change in my own family, where over the course of three generations Forbes became Forbush.)
The other possibility is that someone, not finding arms for Beatty, substituted the arms of a similar-sounding family, Betagh, for them. (I've seen instances of this before, in one 18th century case where the arms of Scholar were attributed to a family named Scolly.)
Whichever the case, Burke's General Armory gives no more information about the original bearer of the arms than Robson does. It being an Irish coat, you might try emailing the Office of the Chief Herald of Ireland to inquire further about the Betagh arms.
David