Varial kickflip = 180 backside shuvit + kickflip
Hardflip = 180 frontside shuvit + kickflip
The hardflip is unique in that it has two main variations. One is the end-over-end style that I think they're describing, where the board only does half a kickflip. The other is "flatter," and explicitly a 180 shuvit with a complete kickflip. In practice the end-over-end style is much more common, easier to perform, and nicer looking.