So the major difference between this and the Harrier is some kind of turbine or rotor in the middle of the thing?
Well, there's more to it than that.
Thrust configuration is different across the board - instead of 4 rotating nozzles, 2/side, feeding from a single engine like on the Harrier, the F-35 has a vectoring nozzle at the rear which can deflect all the way down plus a shaft-driven lift fan.
F-35 is stealthy, and can hit supersonic speeds. Harrier is not and cannot (well, Harriers can, I believe, break the sound barrier in a dive, but it cannot hit and hold supersonic speed in level flight).
Maintenance, a notorious issue with Harriers, is (I believe) supposed to be easier with the F-35.
There's no conventional-takeoff-and-landing version of the Harrier; there is for the Navy's version of the F-35.
The F-35 is much more gawdawful-expensive than the Harrier.