In actual racing boosting, and acceleration are similar. This game throws that out the window and puts them in different categories.
Acceleration: how quickly one is able to gain the boost ability through drift.
Boost: once given the ability, power up, or launch pad, this stat is the speed of the boost you are given.
So basically the acceleration stat will determine how quickly you can earn the boost. And the boost stat basically indicates the speed of the boost.
This seems confusing, but it easily explainable. I am a huge fan of racing, so thought this was slighlty odd, but then once figured out, it makes some sense.