You may be confusing some terms.
"Source" synchronous and a "System" synchronous are Input/Output (IO) concerns. In source synchronous, the source provides a clock and the data that is valid with the provided clock. RGMII and DDR2/3 and many high-speed parallel ADC/DACs are examples.
System Synchronous is more of a legacy, lower speed method. In this case a third party (external osciallator is common) provides the clock to both the transmitting and recieving party. eg, an oscillator provides a 33MHZ clock to your ASIC as well as an external RAM.
System synchronous has issues for higher speeds. For example, lets say an external oscillator gives a 1000MHz clock to both your ASIC and an external DAC. You must receive the 1000MHz clock and output data from your ASIC with an appropriate delay for the clock received at the external DAC. Now even small differences in the clock routing become important.
A synchronous design itself is just one were operation occur on clock edges only, and not on other signal changes/levels.