I believe this is the difference - DRM is an umbrella term that covers the whole class of technology that protects digital data - either hardware or software based. Your monitor is not involved, but the cabling is.
HDCP is one of the possible components of DRM. Simply being able to support HDMI cabling (which supports HDCP) makes something DRM. As far as I know, all electronic devices that can playback digital media made in recent years are supposed to support DRM to keep you from stealing encrypted content.
HDCP is hardware supported digital protection - in this case the DVI or HDMI cabling. One example of the problems with DRM is that not all versions of HDMI supports HDCP correctly - I believe it is completely supported on HDMI versions 1.2 and above. That is one of the reasons many older HD televisions have problems with newer HDMI/DVI between devices - and why my old PC monitor at home does not work directly with my PVR, even though it accepts the cabling hardware - it doesn't read it correctly unless if it goes through my PC card interface which recognizes the newer HDMI version which correctly supports HDCP.
I have had no issues playing back videos I downloaded from the Internet, both encrypted and non, so I am not really sure what the fuss is yet. There have been rumors that Vista reports back all media that has encryption back to Microsoft, but I don't believe that yet. However, I'm sure I'll find out soon enough.