What is the difference between DLNA and UPNP?

UPnP and DLNA are two different standards.

DLNA is derived from UPnP, as an attempt to normalize media interoperability. It does this partly by being more restrictive than UPnP (e.g. by restricting the number of media formats) and partly by adding features (like DRM, i.e. copy protection).

DLNA guidelines can be thought of as an umbrella standard that defines how the home network interoperates at all levels.

From the DLNA whitepaper (pdf).

The UPnP A/V spec provided a strong and flexible means to share content throughout the home, but because UPnP offered rather overwhelming flexibility in the choices vendors and providers could make in configuring their products and services, (push vs. pull, what types of video and audio file formats have to be supported, etc.) the DLNA developed its own interoperability guidelines to simplify the process.

From http://www.broadband2.com/usingstandardstostandout.asp

I couldn't find a clear answer on whether pure UPnP and pure DLNA devices are directly interoperable today, but in 2006 they weren't (pdf). My bet would be "probably not", unless at least one of the devices can handle both.

A UPnP device can stream from a DLNA server just fine.

A DLNA device MAY be able to stream from a UPnP server. Since DLNA is effectively a subset of UPnP, it's possible the UPnP server may offer a format that your DLNA device doesn't recognize and/or support.

But in practice, they're roughly synonymous.

From Wikipedia: DLNA

DLNA uses Universal Plug and Play (UPnP) for media management, discovery and control.[4] UPnP defines the types of device that DLNA supports ("server", "renderer", "controller") and the mechanisms for accessing media over a network. The DLNA guidelines then apply a layer of restrictions over the types of media file format, encodings and resolutions that a device must support.

From Wikipedia: UPnP

Universal Plug and Play (UPnP) is a set of networking protocols that permits networked devices, such as personal computers, printers, Internet gateways, Wi-Fi access points and mobile devices to seamlessly discover each other's presence on the network and establish functional network services for data sharing, communications, and entertainment. UPnP is intended primarily for residential networks without enterprise class devices.