The difference is that antimatter annihilates with any normal matter that it comes into contact with. This means you can't just put it in a tank, the way you can with hydrogen. You can't e.g. combine it with some metal to make a metal hydride to make it safer to store, the way you can with hydrogen.

At an absolute minimum, you need extremely strong magnetic confinement and an extremely hard vacuum. And even then, you're going to get collisions with stray atoms and annihilation events which release gamma rays and other radiation products - although shielding is probably the least of your worries in this scenario.

A typical research lab at a university or large corporation can't make a vacuum strong enough to store even tiny quantities of antimatter for more than a few minutes, and they can't produce the magnetic confinement strength required to store macro quantities of it, either.

So the question with an antimatter-powered car is not if it's going to destroy the surrounding region and bathe it in hard radiation, but how many milliseconds (or less) it will take before that inevitably happens.

But probably luckily for us, this is all moot, because we have no way of producing enough antimatter for this to be an issue. If all the antimatter that's ever been created by humans annihilated simultaneously, only scientists monitoring their instruments closely enough would notice, because it's such a microscopic amount.

Edit: for perspective, you'd need about 7 billion times the 92 antiprotons transported in the truck in the story to produce the energy produced by a single grain of gunpowder.

Liquid gasoline does not spontaneously explode like an action movie. You can put a match in the fuel tank and (presuming infinite oxygen availability) it'd just start a small fire. Heck, may even just give a little puff and then put out the match.

Antimatter in any sufficient fuel quantity, the moment it breaks confinement, will completely annihilate and release ALL it's energy in a single moment, setting off a chain reaction to the remaining antimatter. It's like sitting on an armed nuclear bomb, where you rely on electrified, highly sophisticated containment equipment never failing a single time for months to years... In a radiation-heavy environment known for causing sophisticated electronics to have errors.

And, yes, hydrogen cars were looked at critically because of the perception they can Hindenburg (I'm unsure if it's true or not). Which is a good example because you don't particularly see any hydrogen blimps anymore - we made them illegal because they're dangerous.