From the very first google/linux hit "difference between core fonts and xft":
At the present time, X.org and XFree86 use two font subsystems, each with different characteristics:
The original (15+ year old) subsystem is referred to as the "core X font subsystem". Fonts rendered by this subsystem are not anti-aliased, are handled by the X server, and have names like:
The newer font subsystem is known as "fontconfig", and allows applications direct access to the font files. Fontconfig is often used along with the Xft library, which allows applications to render fontconfig fonts to the screen with antialiasing. Fontconfig uses more human-friendly names like:
Over time, fontconfig/Xft will replace the core X font subsystem. At the present time, applications using the Qt 3 or GTK 2 toolkits (which would include KDE and GNOME applications) use the fontconfig and Xft font subsystem; most everything else uses the core X fonts.
In the future, Linux distributions may support only fontconfig/Xft in place of the XFS font server as the default local font access method.