The Creating a single raster base map option will export your entire project to a TIF file (asking you to specify a resolution) and import that TIF file into Surfer as a single georeferenced base map. You will not be able to edit the image components once it is in Surfer.
The Exporting individual objects option will create a separate base layer for each image, polyline, and polygon in the Didger project and create a separate post layer for all the points in the project. All the base layers and post layers will be overlaid into a single map object in Surfer. The images will be exported from Didger in 300 dpi resolution (using the physical size under Map | Project Limits) and polylines and polygons will be exported to DXF files. This allows you to edit the individual objects even after they are imported into Surfer.
Updated October 12, 2016