Carrier based correlation requires a little more hardware, a bandpass filter and a detector, but the principles are the basically same. Two signals are applied to the multiplier. This is the clever part of SS systems. The data is modulated on the transmitted signal such that for correlation and tracking purposes the data part of the signal can be essentially ignored. Once we have correlation we can get that data because the multiplication part of the correlation process strips off our noise like signal and leaves just the data that was hidden inside this signal.
Lets look at how the correlator works.
The correlator is essentially comparing the two signals. What we now have is a way of measuring how close we are to perfect synchronization. With a little more circuitry one can build a system that uses the output of the correlator to automatically recognize correlation. It has to do with the very nature of the signals used in SS systems. SS systems generally transmit noise like signals with the data we want to receive embedded in them.