The transmitter is what you hold in your hand. The box in the truck is the receiver. They match. It's not the radio that's the issue, I don't think, it's the esc (throttle), since you have steering. That combo on hobbypartz will probably work better for you, especially since it has the manual so you'll know what you're doing. I personally don't have any experience with that brand, I've only bought hobbywing stuff there, but there are others on the forum that have bought leopard stuff with no issues.
Since this is just a basher, there's no point in getting something more $$ or sophisticated. You could also just pick up a cheap brushed ESC somewhere, since there's probably nothing wrong with the motor you have. I'm assuming you wouldn't mind going cheap, considering the car you started with. Brushed escs can be found for $30-40, even by major brands (HPI, Traxxas).