A liftback is a variation of a hatchback car body style, with a more gently sloping roofline, roughly between 45 and 10 degrees, whereas traditional or archetypal hatchback designs tend to use a 45 degree to near vertical slope on the top-hinged tailgate.
1973 Toyota Celica, the world's first "liftback", in this case a fastback-styled hatchback
Skoda Rapid liftback. Note how the tailgate is hinged from the roof and the rear window is lifted along with the rest of the tailgate. It is not a fastback as it does not have an uninterrupted slope in the roofline.
A 1974 Leyland P76. It can be considered both a liftback (the tailgate is hinged from the roof) and a fastback (the roofline is an uninterrupted slope).
Image: Opel Vectra C 2.2 Direkt rear
A hatchback is a car body configuration with a rear door that swings upward to provide access to the main interior of the car as a cargo area rather than just to a separated trunk. Hatchbacks may feature fold-down second-row seating, where the interior can be reconfigured to prioritize passenger or cargo volume.
Volkswagen Golf 5-door hatchback
Mini Hatch 3-door hatchback
2017 Citroën C3 pictured, a tailgate hinged at the roof is a predominant characteristic of hatchbacks, estates/station wagons, and liftbacks
Hyundai i30 as a conventional 5-door hatchback