What are the differences between intertank valve and crossfeed valve? Regarding the fuel system in an aircraft, I read that there are two valves: the intertank valve and the crossfeed valve. 

They are both motor driven butterfly type valve which function is to allow fuel from the left and right hoppers to combine. 

What are the differences between them?
In layman's terms, at least on a Gulfstream G450/G550, the cross-feed system allows the engines to be fed from either the left tank, the right tank, or both tanks (one to each engine.) the cross-feed pipes feed into the fuel hoppers, not directly into the other tank. While you can use the cross-feed system to fix a fuel imbalance, doing so would be via using the fuel (in the engines) not actually transferring it from tank to tank.

The intertank system is a valve and pipe system between the tanks themselves, allowing a fuel imbalance to be fixed by initiating/allowing the transfer of fuel from tank to tank directly.

My sources were:
G450/G550 Fuel System
G450/G550 Fuel Unbalanced