Dial up internet used an analog transfer domain to encode the information. DSL does not, and is an entirely different technology (and is not 'dial-up').
56kbps modems and the like relied on digital telephone lines. I'm not sure where the 30kbps number comes from though - earlier pre-digital modems did go faster than that. Although you could argue those were 'pre-internet' as well...
If you're defining the 'channel' as 'local copper pair', then, sure?
But the other end of the local copper pair switched and became digital, which changes the channel in my eyes at least. There was then a series of bandwidth increases in the digital realm, giving significantly more efficient and effective use of the channel.
It's not the same channel, because DSL requires equipment fairly close to the subscriber. You can't transmit DSL on telephone utility poles for miles, like you can dialup.
56kbps modems and the like relied on digital telephone lines. I'm not sure where the 30kbps number comes from though - earlier pre-digital modems did go faster than that. Although you could argue those were 'pre-internet' as well...