As the video suggests, yes he was in cheers. No, he wasn't the same caracter.
They had to retcon Frasier's back story for the spin off, as he had previously claimed not to have a brother and that his father was dead.
The latter was explained during Ted Danson's cameo in Frasier as being a throwaway comment made after having an argument with his dad on the phone. I can't remember if they addressed the claims to be an only child.
Interestingly (okay, that's subjective) Kirstie Alley is the only member of the main Cheers cast not to cameo in Frasier. Not because of any bad blood; she refused the offer because as a scientologist she cannot be seen to endorse psychiatry.