A Custom 24 Standard will be all mahogany, while the 24-08 will be a mahogany body with a maple top...so you'll certainly notice a different acoustic vocal character between the two guitars. Depending on your play style, rig, and gear you may or may not be able to tell much of a difference plugged in - for example, running a ton of gain or modular effects can mask or bury a guitar's natural vocal character.
That being said, the tone, pick attack, and sustain can vary from guitar to guitar regardless of build, make, or model.
EDIT: I just realized that you may have meant Custom 24 "standard" as in, run-of-the-mill Custom 24. In which case, switching and electronics (pickups?) will really be the only difference - save for maybe build specifics like a rosewood or maple neck in some sort of Wood Library run. Both have maple tops with mahogany bodies, mahogany necks, and rosewood boards. Both will be 25" scale length, as well.