The fancy names and the layering makes it a little tricky to understand. The core of the imaging model is called Quartz. It provides support for rendering 2D shapes and text. Its graphics rendering functionality is exported through the Quartz 2D API, which is implemented in Core Graphics. Quartz is also used for window management: the Quartz Compositor, a lightweight window server, is implemented partly in the WindowServer application and partly in the Core Graphics framework. Quartz 2D uses PDF as the native format for its drawing model. In other words, it stores rendered content internally as PDF, which facilitates features such as automagic PDF screenshots, export/import of PDF data natively, and rasterizing PDF data. Quartz 2D also does device-independent and resolution-independent rendering of bitmap images, vector graphics, and anti-aliased text. NEXTSTEP's window server was based on Display PostScript, so was Sun's NeWS (~1986).
NeWS wasn't based on DPS. It's a full display server based on the PostScript Red Book with some extensions (canvases, lightweight processes and sync primitives, events, classes, garbage collection). This allows to write applications in this extended PostScript or in other programming languages, using a preprocessor, such as cps for C or lps for Scheme-48 and Allegro LISP, that generates PS snippets that get sent to the server.
