Well they are conpletely different weapons unlike most rifle and carbine model variants so the distinction on how they are issued tended to be based upon what type of service or role the soldier would carry out.

The Garand is a front line infantry weapon, it fires a much larger round the .30-06 which weighs twice as much as the .30 carbine round. Futhermore it has much better range than the carbine. M1 Garand has a maximum effetive range of 500 yards - pdf warning - and most trained soldiers would be effective using the Garand at ranges of 300-400 yard. The carbine only has a range of 150 yards, so if you were going to be in frequent combat in open areas, the carbine would not be an effective combat weapon.

However, to give you a really brief answer for now:

Officers and NCOs, as well as airborne and other elite troops were frequently allowed to exchange with Ordnance personnel for their individual weapon of choice.

Rush, Robert S., GI: The US Infantryman in World War II, Osprey Publishing Ltd. (2003), ISBN 1-84176-739-5, pp. 33–35

So yes, it was possible to switch out if needed, although doing so in certain combat situations would be a terrible mistake.

I've always wondered this as well. Why were certain men assigned certain weapons? Is it body size or strength or something?