Baseband is digital (1s & 0s), but everything on that cable to be transmitted or received must use that one channel. That one channel is very fast, so each device needs only to use that high speed channel for only a little of the time.
An analog modem (your 56k dial-up)communicates over regular telephone lines by converting computer (digital) data into sound. At the receiving end, the data must then be converted back to digital. The speed of the analog modem is very slow compared to digital modems.
ISDN: Integrated Services Digital Network and is a system of digital phone connections which allows voice and data to be transmitted simultaneously across the world using end-to-end digital connectivity. There are two basic types of ISDN service: Basic Rate Interface (BRI) and Primary Rate Interface (PRI). BRI (what I use, consists of two 64-Kbps B-channels and one D-channel for transmitting control information) is a basic service is intended to meet the needs of most individual users. PRI (consists of 23 B-channels and one D-channel (U.S.) or 30 B-channels and one D-channel (Europe))is intended for users with greater capacity requirements.
These versions of ISDN employ baseband transmission. Another version, called B-ISDN, uses broadband transmission and is able to support transmission rates of 1.5 Mbps. B-ISDN requires fiber optic cables and is not widely available.
That definition isn't the end all be all. Afterall, not that long ago, Diamond was selling software that used Dual Modems. It could carry multiple data channels simultaneously. That CLEARLY isn't broadband. The FCC considers Broadband to be any connection that meets or exceeds 200kbps in both directions. Clearly ISDN BRI does not meet that standard. Also, if you've ever used an ISDN BRI connection you wouldn't think it was Broadband either. Certainly better than a dialup, but the best download rate you can get is about 13-14k/sec. That's only about 2.3 times the speed of a 56k Dialup.
As I noted in my original post, there are varying definitions depending on who you talk to. Most will agree that it's only at somewhere north of 200kbits that you're into Broadband access as related to the internet.