Circuit identification code
The ISDN Services User Part (ISUP) Circuit Identification Code (CIC) in the Initial Address Message (IAM) consists of a range of 0 to 65,535. On the signalling path the CIC provides information about where the voice part of the call is carried - on which trunk and in which timeslot.
The Bearer Independent Call Control (BICC) Call Instance Code (CIC) in the IAM consists of a range of 0 to 4,294,967,295.
There can be multiple trunk groups to a given point code using a combination of ISUP and BICC signaling. This means, for example, that CIC 100 on an ISUP trunk group can be replicated using CIC 100 on a BICC trunk group to the same point code. The far end switch distinguishes the difference by referencing the Service Indicator (SI). ISUP uses SI=05 and BICC uses SI=13 in North America.
You can find more details in the ISUP wiki.
A CIC identifies a circuit between two exchanges being set up for voice transmission in a telephone call. The CIC is sent in SS7 ISUP (ISDN User Part) messages (for example, IAM, ACM and ANM) to identify the circuit for voice transmission. Usually the CIC is 14 bits long, so capable of identifying one of 16,384 circuits between two telephone exchanges. The CIC determines on which trunk voice will be transmitted for the call being set up using the messages carrying this particular CIC value.