You use CRS when you want to display the VOR CDI on your EHSI. The CRS knob sets the VOR beam-bar on the required inbound/outbound course.
As 'CRS' is not an actual lateral mode, the CRS setting does not, in itself, affect the AP/FD behaviour; however, if VOR/LOC is the selected lateral model, then the CRS setting will determine the track that the AP/FD follows.
You use HDG if you want the AP/FD to follow the selected heading. This may be used to fly a non-precision approach when LNAV is not available.
Remember that whatever you set on the MCP, it is the FMA that will tell you what the AP/FD is actually referring and following.