CoreGraphics.framework
QuartzCore.framework
Quartz.framework
OS X only
All three frameworks use OpenGL underneath because all drawing in iOS or OS X goes through OpenGL at some point. See the section Media Layer Frameworks of the Mac OS X Technology Overview for details.
Other "Quartz" technologies you may have heard of:
These are internal implementations of GPU rendering, not APIs. They decide whether to create the window buffer in the CPU and only use OpenGL to upload as a texture (the default) or to do the whole rendering using OpenGL, which not always improves performance. You can alternate between the two using the QuartzGLEnable Info.plist setting. For an explanation see John Siracusa review of Mac OS X 10.4 Tiger, pages 13 and 14.
“Quartz” and “Core” are marketing names sprinkled over frameworks and APIs in a random manner. If they wanted to create a confusing naming mess, they succeeded.