In Synth Mode (TX), the synthesizer is settled to the channel frequency and the time for which it will remain in this state the synthesizer will remain tuned to this frequency. If we switch to the sleep state then the synthesizer will be switched OFF and it needs to be settled down again before transmitting.
Synth Mode (RX) is used when we are using the different frequency for transmission and reception. Before switching to the Receive mode device will switch to the Synth Mode (RX). In this the synthesizer will tune to the frequency required. Once the frequency is tuned to the Receive Frequency then the device will switch to Receive mode for reception of data, whenever required. Thus, eliminating the delay required to switch the frequency from transmit to receive.