The Core is the hardware that processes the data. The Thread is the path the data is delivered to the Core on.
Generally each core has one thread transferring data to and from it. In the case of Hyperthreading each core has 2 threads moving data to and from them therefore doubling the processing of each core effectively doubling the core count. For example the i7 4790 has 4 physical and 4 virtual cores due to hyperthreading.