What is the difference between an intranet and a DMZ, and what kind of addressing does each use?

Question

Accepted Answer

The intranet is the internal network and uses private (RFC 1918) addresses; the DMZ holds internet-facing servers, which need public IPv4 addresses.
Intranet: a company's internal network. Typically addressed from a private block such as 10.0.0.0/8, subnetted on /16 or /24 boundaries. Reaches the internet through NAT.
DMZ (demilitarized zone): the segment holding internet-facing servers (web, mail, etc.). Because outside clients must reach these servers directly, DMZ devices are configured with public IPv4 addresses (often presented via NAT).
Why it matters: separating the DMZ from the intranet lets you apply tighter security policy to publicly reachable servers without exposing the internal network.
Go deeper:

DMZ (computing) (Wikipedia) — the buffer subnet for internet-facing servers and why it's isolated.
 Intranet (Wikipedia) — the internal-only network that uses private addressing.