HDR: High Dynamic Range. You take more than one shot at different exposures to capture all the light detail you want. Software then combines them and you can then map it into something that can be displayed.
I haven't tried it on the moon, but in general you ideally need to take the shots without moving the camera. As the moon itself is moving, you should do it quickly.
So with your two shots, assuming they were aligned, software would be able to map the dynamic range into something visible and keep both the treeline and moon detail.
_________________Canon DSLRs: 7D2, 7D1, 5D2, 1D, 600D, 450D full spectrum, 300D IR mod
Lenses: EF 35/2, 85/1.8, 135/2+SF, 70-300L, 100-400L, 100L, MP-E 65, EF-S 10-18, 15-85
3rd party: Zeiss 2/50 makro, Samyang 8mm fisheye, Sigma 50/1.4A, 150 macro, 120-300 f/2.8 OS
Compacts: Sony HX9V, Fuji X100.