PIXEL refers to the default desktop environment on the official distributions of Raspbian.
[Note that the Pi Foundation no longer uses this name, but the software still exists as the default desktop on Raspbian. Since "The desktop environment formerly known as PIXEL" doesn't fit in a tag, this will have to do.]
LXDE is a POSIX compliant desktop environment used on Raspbian; in September 2016 the Raspberry Pi Foundation announced a fork, PIXEL, to be used in as the default in their distributions of Raspbian.
