Functionally, there is no difference between a cut thread and a rolled thread. The difference enters in the manufacture of the bolt. Using 1” anchor bolts as an example the processes are:
Cut thread is created by a process that cuts away the steel from the round bar to form the threads. To cut thread, the process begins with a full 1” diameter round bar. The threads are cut into the round bar resulting in an anchor bolt with 1” diameter threads and a body of 1” diameter.
Rolled thread is created by a process that extrudes steel from the surface of the round bar to form the threads. To roll thread, the process begins with .912” round bar. The round bar is rolled through a set of dies that displace the steel to form the threads. The result is a bolt with 1” diameter thread and a .912” body.
Cut thread meets all ASTM specifications. Rolled thread meets ASTM specifications with the exception of A325 and A490. However, one thing to remember is that Architects and Engineers often specify cut thread for anchor bolts. Cut thread can usually be substituted for rolled thread but the opposite may not always be true.