"Put the display to sleep" and "Switch off the display" are different DPMS modes.
There are four DPMS modes:
- Normal: what your monitor is doing when you're using it
- Standby: a power saving mode, the screen is blanked by turning the RGB guns off
- Suspend: another power saving mode, similar to standby, but the power supply to the monitor is also turned off, saving even more power
- Off: the monitor is actually turned off, except for a circuit that listens for a signal to turn it back on; it uses almost no power, but it takes longer to turn back on than the other power saving modes
There are more technical details, including the watts used in each mode, here.
Xfce's "Put the display to sleep" is either DPMS standby or suspend, I'm not sure which. "Switch off the display" uses DPMS off mode.
Now, these DPMS modes clearly only have meaning for CRT monitors. LCD monitors interpret DPMS signals differently. It might depend on the monitor, but there is probably no difference for LCD monitors. They just turn off if they receive any of the DPMS power saving signals.
Which setting should you use, then? Again, it probably doesn't matter. I would use "Switch off the display", since that's actually what I want my monitor to do. Telling your monitor to go into a CRT power saving mode when you know it's just going to turn off anyway seems a bit backwards to me.