The biggest difference for long sprinters (200/400) is the heel, and the biggest difference is keeping the heel up easier going around curves, and the 400 (because you are running one of the curves close to top speed, not right out of the blocks) is one place where you will see this difference. Distance spikes are actually not that bad for 100, but as soon as you try to sprint around a curve, they slow you down.
For shorter sprinters there are two other differences:
(1) Harder plate which means higher energy return, and that means better speed maintenance at the end of 100 and 200.
(2) Placement of spike receptacles to provide better traction coming out of blocks.
Sprint spikes are not necessarily a lot heavier, just that Nike is selling old-style junky ones to the public. Mine (Asics Japan Lite-ning) is 5 ounces, and by comparison the Nike sprint spikes feel like a Brooks Beast. Adidas has a couple lighter than that (but the lightest one is over $200). Usain Bolt's signature spike from Puma is also lighter than the Nike spikes.
The ones with no heel tend to require better biomechanics from the athlete. And you do not need a full-length plate, although that is the new design style.