Similar but not really identical meaning.

When something is synchronous, you have a third factor involved, that stands for the synchronization.

In SPI, the MOSI and MISO signals are updated synchronously, controlled by the clock signal.

Correlated normally means that one action may result in a side effect. Statistics uses the term correlation to define how closely a variable B gets affected by a change to variable A.

The activation of a transistor may result in noise on the power lines.

When you open the door to the refridgerator, you normally see an increase in the temperature in the fridge.

You may see a correlation beteen the power consumption of a processor, and the number of transfers / second on the SPI bus.

Detecting correlations between different events can be quite hard. Especially since there may be even more factors involved. Are you screaming because you are deaf or are you deaf because you have been screaming too much. Or are you deaf and used to screaming because you have spent too much time at a night club?