Well, I don't have experience with these specific types of shoes, but I do have several years of working in retail shoe stores, so will take an educated guess on this one. Most likely, track shoes are geared towards running, so will be slightly curved to aid in the running motion, will have soles that grip the ground, and will have cushioning mainly in the heels to absorb the shock of running. High jump shoes are probably more flexible to accommodate the motion of jumping, and probably have cushioning at the ball of the feet, to absorb shock upon landing, which most likely occurs at the ball of the foot.
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Normal track shoes have spikes on the bottom of both shoes although, with high jump shoes the non-jumping foot shoe has no spikes. To allow for your foot to be lifted off the ground faster.