Figuring out how to define hard trance is about as difficult as looking at the name of the genre and making assumptions based on that. Hard trance is trance, but harder.
Hard trance is usually sits anywhere between 136-155bpm. It has fairly close relationships with tech trance and uplifting trance, in which hard trance tracks can often borrow elements of both and act as a middle ground between the two. It takes the aggressive synthetic sounds from tech trance, and the melodic focus from uplifting trance, while providing it's own twist with big full kicks and driving basslines.