The authentication in DSL is essentially an backward compatibility hack. Original motivation for that was compatibility with Radius/Diameter based AAA systems of ISPs (and to lesser extent the fact that the link the looks from both sides like faster dialup connection). Today it is used mostly because it is default. In many cases ISP (or even the underlying telco) either uses one login/password for all customers or simply accepts anything.
All DSL lines have same L2 interface as ATM and thus there is no authentication. How the authentication works is that PPP gets tunelled through this, either by running PPP directly on AAL5 (PPPoA), or more commonly and somewhat nonsensically by tuneling by wrapping PPP in ethernet frames that are then transfered inside AAL5 channel (PPPoE, or more correctly PPPoEoA). Interestingly this is usually used only on the first virtual channel (ie. the "Internet" one) and not on the additional channels that you typically get today (IPTV, VoIP, free hotspots...), these additional channels are usually straight Ethernet over AAL5 with the modem behaving like simple L2 bridge (often these channels form relatively large broadcast domains that are typically NATed to the Internet).
[Edit:] In contrast, DOCSIS variants for Internet over CaTV are derived directly from IEEE 802 family of technologies and there are no telco-style ATM/X.25/whatever protocols in between. Good first approximation is that the DOCSIS segment handled by one CMTS behaves like one big ethernet switch. But beacuse of the nature of shared medium, data on the coaxial cable is encrypted as otherwise it would be trivial to eavesdrop on anyone else on the same segment. The encryption even involves PKI to mutually authenticate modem and CMTS.
On DSL there is clear physical interface on the network side, that can be turned on or off, shaped and metered which is everything that the ISP cares about from the charging and authentication PoV. CaTV does not have anything like that and thus there has to be relative complex authentication and confidentiality mechanism (that is, somewhat paradoxically, usually completely invisible to the end user).